SlideShare a Scribd company logo
NON LINEAR
DYNAMICAL SYSTEMS
VIKRAM SINGH SANKHALA
ISOLATED SYSTEM
• Zero interaction with environment.
• In Real World it is difficult to isolate a system from its Environment
NON LINEAR SYSTEMS
• Multiple Inputs
• Feedback Loops
• Error grow Exponentially
• Sensitivity to Initial Conditions
DISTRIBUTED SYSTEMS
• Multiple Interacting Non Linear Dynamic Systems as Components
MODELLING NON LINEAR DYNAMICAL SYSTEMS
• Stochastic noise-driven linear and nonlinear dynamical systems.
• Another approach involves a state space where time series observations are
transformed to the phase space vectors. They model the dynamics of a system by
modeling the dynamics of the corresponding points in the phase space using a
Mapping Function
• The Mapping Function can be used for Prediction of future states.
DIMENSION REDUCTION
• Principal Components Analysis – Linear Method
• Non Linear Techniques are also there
ALGORITHMIC METHODS
• As soon as you introduce self-loops in your model structure, you introduce time,
and therefore the system becomes dynamical.
• In many statistical models, we don't have a closed form solution for inference on
particular variables, so we must use iterative/algorithmic methods to approximate
/ sample values.
• Neural Networks play an important role for modelling Dynamic non linear
systems.
ARTIFICIAL NEURAL NETWORKS
• Consist of Connected local processing elements (neurons)
• These accept weighted inputs from other such elements
• They use these weighted inputs to give a single output
FREEMAN 1991
• Artificial neural systems were designed to capture some of the useful brain
functions by modeling the features of the brain.
• Chaos "may be the chief property that makes the brain different from an artificial-
intelligence machine“.
CHAOS
• Chaos is statistically indistinguishable from randomness, and yet it is deterministic
and not random at all.
• A chaotic system will produce the same results if given the same inputs
• But you can not predict in what way the system's behavior will change for any
change in the input to that system
• It is random appearing, and yet has a large degree of underlying order.
BUTTERFLY EFFECT
• Affects Initial Conditions
• Initial Condition inaccuracy grows exponentially.
• We get extra ordinary and Counter Intuitive Results
CHAOS ENGINEERING
• How Emergent behavior from Component Interactions can cause the system to
devove into Chaotic state,
• Controlled Experiments on Distributed Systems by introducing failure.

More Related Content

What's hot

NONLINEAR CONTROL SYSTEM (Phase plane & Phase Trajectory Method)
NONLINEAR CONTROL SYSTEM(Phase plane & Phase Trajectory Method)NONLINEAR CONTROL SYSTEM(Phase plane & Phase Trajectory Method)
NONLINEAR CONTROL SYSTEM (Phase plane & Phase Trajectory Method)
Niraj Solanki
 
Chaos Theory: An Introduction
Chaos Theory: An IntroductionChaos Theory: An Introduction
Chaos Theory: An Introduction
Antha Ceorote
 
Bifurcation
BifurcationBifurcation
Bifurcation
Hamed Abdi
 
Chaos1
Chaos1Chaos1
Chaos Theory
Chaos TheoryChaos Theory
Chaos Theory
Camila Valbuena
 
Fuzzy Logic in the Real World
Fuzzy Logic in the Real WorldFuzzy Logic in the Real World
Fuzzy Logic in the Real World
BCSLeicester
 
Introduction to mathematical modelling
Introduction to mathematical modellingIntroduction to mathematical modelling
Introduction to mathematical modelling
Arup Kumar Paria
 
Recurrence Quantification Analysis : Tutorial & application to eye-movement data
Recurrence Quantification Analysis :Tutorial & application to eye-movement dataRecurrence Quantification Analysis :Tutorial & application to eye-movement data
Recurrence Quantification Analysis : Tutorial & application to eye-movement data
Deb Aks
 
Maths partial differential equation Poster
Maths partial differential equation PosterMaths partial differential equation Poster
Maths partial differential equation Poster
Er. Ashish Pandey
 
Chaos
ChaosChaos
The monte carlo method
The monte carlo methodThe monte carlo method
The monte carlo method
Saurabh Sood
 
Mathematical modelling
Mathematical modellingMathematical modelling
Mathematical modelling
NandiniNandus
 
Mathematical Modeling for Practical Problems
Mathematical Modeling for Practical ProblemsMathematical Modeling for Practical Problems
Mathematical Modeling for Practical Problems
Liwei Ren任力偉
 
Stochastic Process
Stochastic ProcessStochastic Process
Stochastic Process
knksmart
 
MILNE'S PREDICTOR CORRECTOR METHOD
MILNE'S PREDICTOR CORRECTOR METHODMILNE'S PREDICTOR CORRECTOR METHOD
MILNE'S PREDICTOR CORRECTOR METHOD
Kavin Raval
 
Mathematical modeling
Mathematical modelingMathematical modeling
Mathematical modeling
Dr. Deepak Kumar
 
Firefly Algorithms for Multimodal Optimization
Firefly Algorithms for Multimodal OptimizationFirefly Algorithms for Multimodal Optimization
Firefly Algorithms for Multimodal Optimization
Xin-She Yang
 
Lecture 6 modelling-of_electrical__electronic_systems
Lecture 6 modelling-of_electrical__electronic_systemsLecture 6 modelling-of_electrical__electronic_systems
Lecture 6 modelling-of_electrical__electronic_systems
Saifullah Memon
 
03 dynamic.system.
03 dynamic.system.03 dynamic.system.
03 dynamic.system.
Mahmoud Hussein
 
Introduction to MCMC methods
Introduction to MCMC methodsIntroduction to MCMC methods
Introduction to MCMC methods
Christian Robert
 

What's hot (20)

NONLINEAR CONTROL SYSTEM (Phase plane & Phase Trajectory Method)
NONLINEAR CONTROL SYSTEM(Phase plane & Phase Trajectory Method)NONLINEAR CONTROL SYSTEM(Phase plane & Phase Trajectory Method)
NONLINEAR CONTROL SYSTEM (Phase plane & Phase Trajectory Method)
 
Chaos Theory: An Introduction
Chaos Theory: An IntroductionChaos Theory: An Introduction
Chaos Theory: An Introduction
 
Bifurcation
BifurcationBifurcation
Bifurcation
 
Chaos1
Chaos1Chaos1
Chaos1
 
Chaos Theory
Chaos TheoryChaos Theory
Chaos Theory
 
Fuzzy Logic in the Real World
Fuzzy Logic in the Real WorldFuzzy Logic in the Real World
Fuzzy Logic in the Real World
 
Introduction to mathematical modelling
Introduction to mathematical modellingIntroduction to mathematical modelling
Introduction to mathematical modelling
 
Recurrence Quantification Analysis : Tutorial & application to eye-movement data
Recurrence Quantification Analysis :Tutorial & application to eye-movement dataRecurrence Quantification Analysis :Tutorial & application to eye-movement data
Recurrence Quantification Analysis : Tutorial & application to eye-movement data
 
Maths partial differential equation Poster
Maths partial differential equation PosterMaths partial differential equation Poster
Maths partial differential equation Poster
 
Chaos
ChaosChaos
Chaos
 
The monte carlo method
The monte carlo methodThe monte carlo method
The monte carlo method
 
Mathematical modelling
Mathematical modellingMathematical modelling
Mathematical modelling
 
Mathematical Modeling for Practical Problems
Mathematical Modeling for Practical ProblemsMathematical Modeling for Practical Problems
Mathematical Modeling for Practical Problems
 
Stochastic Process
Stochastic ProcessStochastic Process
Stochastic Process
 
MILNE'S PREDICTOR CORRECTOR METHOD
MILNE'S PREDICTOR CORRECTOR METHODMILNE'S PREDICTOR CORRECTOR METHOD
MILNE'S PREDICTOR CORRECTOR METHOD
 
Mathematical modeling
Mathematical modelingMathematical modeling
Mathematical modeling
 
Firefly Algorithms for Multimodal Optimization
Firefly Algorithms for Multimodal OptimizationFirefly Algorithms for Multimodal Optimization
Firefly Algorithms for Multimodal Optimization
 
Lecture 6 modelling-of_electrical__electronic_systems
Lecture 6 modelling-of_electrical__electronic_systemsLecture 6 modelling-of_electrical__electronic_systems
Lecture 6 modelling-of_electrical__electronic_systems
 
03 dynamic.system.
03 dynamic.system.03 dynamic.system.
03 dynamic.system.
 
Introduction to MCMC methods
Introduction to MCMC methodsIntroduction to MCMC methods
Introduction to MCMC methods
 

Similar to Non linear dynamical systems

Presentationnnnn
PresentationnnnnPresentationnnnn
Presentationnnnn
Sulman Ahmed
 
Chaos Presentation
Chaos PresentationChaos Presentation
Chaos Presentation
Albert Yang
 
Industry Training: 03 Awareness Simulation
Industry Training: 03 Awareness SimulationIndustry Training: 03 Awareness Simulation
Industry Training: 03 Awareness Simulation
FET AWARE project - Self Awareness in Autonomic Systems
 
System Simulation and Modelling with types and Event Scheduling
System Simulation and Modelling with types and Event SchedulingSystem Simulation and Modelling with types and Event Scheduling
System Simulation and Modelling with types and Event Scheduling
BootNeck1
 
CONTROL SYSTEMS.pptx
CONTROL SYSTEMS.pptxCONTROL SYSTEMS.pptx
CONTROL SYSTEMS.pptx
EEEACEEC
 
Introduction to Hamiltonian Neural Networks
Introduction to Hamiltonian Neural NetworksIntroduction to Hamiltonian Neural Networks
Introduction to Hamiltonian Neural Networks
Miles Cranmer
 
The Hurricane's Butterfly: Debugging pathologically performing systems
The Hurricane's Butterfly: Debugging pathologically performing systemsThe Hurricane's Butterfly: Debugging pathologically performing systems
The Hurricane's Butterfly: Debugging pathologically performing systems
bcantrill
 
Artificial Neural Network Seminar Report
Artificial Neural Network Seminar ReportArtificial Neural Network Seminar Report
Artificial Neural Network Seminar Report
Todd Turner
 
neuralnetwork.pptx
neuralnetwork.pptxneuralnetwork.pptx
neuralnetwork.pptx
SherinRappai1
 
neuralnetwork.pptx
neuralnetwork.pptxneuralnetwork.pptx
neuralnetwork.pptx
SherinRappai
 
Simulation Models as a Research Method.ppt
Simulation Models as a Research Method.pptSimulation Models as a Research Method.ppt
Simulation Models as a Research Method.ppt
QidiwQidiwQidiw
 
Artificial neural network
Artificial neural networkArtificial neural network
Artificial neural network
nainabhatt2
 
Artificial Neural Network
Artificial Neural NetworkArtificial Neural Network
Artificial Neural Network
NainaBhatt1
 
Seminar on Chaos Based Cryptography
Seminar on Chaos Based CryptographySeminar on Chaos Based Cryptography
Seminar on Chaos Based Cryptography
Muhammad Hamid
 
Machine Learning, Stock Market and Chaos
Machine Learning, Stock Market and Chaos Machine Learning, Stock Market and Chaos
Machine Learning, Stock Market and Chaos
I Know First: Daily Market Forecast
 
Course Learning Outcomes Virtual Systems and Services
Course Learning Outcomes Virtual Systems and ServicesCourse Learning Outcomes Virtual Systems and Services
Course Learning Outcomes Virtual Systems and Services
KdmFarooqMurad
 
nil-100128213838-phpapp02.pptx
nil-100128213838-phpapp02.pptxnil-100128213838-phpapp02.pptx
nil-100128213838-phpapp02.pptx
dlakmlkfma
 
nil-100128213838-phpapp02.pdf
nil-100128213838-phpapp02.pdfnil-100128213838-phpapp02.pdf
nil-100128213838-phpapp02.pdf
dlakmlkfma
 
Neural Networks Lec3.pptx
Neural Networks Lec3.pptxNeural Networks Lec3.pptx
Neural Networks Lec3.pptx
moah92926
 
The future is quantum
The future is quantumThe future is quantum
The future is quantum
Aravinth Balaji Ravichandran
 

Similar to Non linear dynamical systems (20)

Presentationnnnn
PresentationnnnnPresentationnnnn
Presentationnnnn
 
Chaos Presentation
Chaos PresentationChaos Presentation
Chaos Presentation
 
Industry Training: 03 Awareness Simulation
Industry Training: 03 Awareness SimulationIndustry Training: 03 Awareness Simulation
Industry Training: 03 Awareness Simulation
 
System Simulation and Modelling with types and Event Scheduling
System Simulation and Modelling with types and Event SchedulingSystem Simulation and Modelling with types and Event Scheduling
System Simulation and Modelling with types and Event Scheduling
 
CONTROL SYSTEMS.pptx
CONTROL SYSTEMS.pptxCONTROL SYSTEMS.pptx
CONTROL SYSTEMS.pptx
 
Introduction to Hamiltonian Neural Networks
Introduction to Hamiltonian Neural NetworksIntroduction to Hamiltonian Neural Networks
Introduction to Hamiltonian Neural Networks
 
The Hurricane's Butterfly: Debugging pathologically performing systems
The Hurricane's Butterfly: Debugging pathologically performing systemsThe Hurricane's Butterfly: Debugging pathologically performing systems
The Hurricane's Butterfly: Debugging pathologically performing systems
 
Artificial Neural Network Seminar Report
Artificial Neural Network Seminar ReportArtificial Neural Network Seminar Report
Artificial Neural Network Seminar Report
 
neuralnetwork.pptx
neuralnetwork.pptxneuralnetwork.pptx
neuralnetwork.pptx
 
neuralnetwork.pptx
neuralnetwork.pptxneuralnetwork.pptx
neuralnetwork.pptx
 
Simulation Models as a Research Method.ppt
Simulation Models as a Research Method.pptSimulation Models as a Research Method.ppt
Simulation Models as a Research Method.ppt
 
Artificial neural network
Artificial neural networkArtificial neural network
Artificial neural network
 
Artificial Neural Network
Artificial Neural NetworkArtificial Neural Network
Artificial Neural Network
 
Seminar on Chaos Based Cryptography
Seminar on Chaos Based CryptographySeminar on Chaos Based Cryptography
Seminar on Chaos Based Cryptography
 
Machine Learning, Stock Market and Chaos
Machine Learning, Stock Market and Chaos Machine Learning, Stock Market and Chaos
Machine Learning, Stock Market and Chaos
 
Course Learning Outcomes Virtual Systems and Services
Course Learning Outcomes Virtual Systems and ServicesCourse Learning Outcomes Virtual Systems and Services
Course Learning Outcomes Virtual Systems and Services
 
nil-100128213838-phpapp02.pptx
nil-100128213838-phpapp02.pptxnil-100128213838-phpapp02.pptx
nil-100128213838-phpapp02.pptx
 
nil-100128213838-phpapp02.pdf
nil-100128213838-phpapp02.pdfnil-100128213838-phpapp02.pdf
nil-100128213838-phpapp02.pdf
 
Neural Networks Lec3.pptx
Neural Networks Lec3.pptxNeural Networks Lec3.pptx
Neural Networks Lec3.pptx
 
The future is quantum
The future is quantumThe future is quantum
The future is quantum
 

More from Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr

Primer on major data mining algorithms
Primer on major data mining algorithmsPrimer on major data mining algorithms
Primer on major data mining algorithms
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Vikram emerging technologies
Vikram emerging technologiesVikram emerging technologies
Blockchain concept explained
Blockchain concept explainedBlockchain concept explained
Hyperloop explained
Hyperloop explainedHyperloop explained
Vikram budget 2018
Vikram budget 2018Vikram budget 2018
Vikram cgst updated budget 2018
Vikram cgst updated budget 2018Vikram cgst updated budget 2018
Vikram cgst updated budget 2018
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Basic health facts presentation by vikram
Basic health facts presentation  by vikramBasic health facts presentation  by vikram
Basic health facts presentation by vikram
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Gst simplified vikram sankhala
Gst simplified vikram sankhalaGst simplified vikram sankhala
Gst simplified vikram sankhala
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Paper -future_of_finance_function
Paper  -future_of_finance_functionPaper  -future_of_finance_function
Paper -future_of_finance_function
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Transfer pricing 2013 sept 20th by vikram singh sankhala
Transfer pricing 2013 sept 20th by vikram singh sankhalaTransfer pricing 2013 sept 20th by vikram singh sankhala
Transfer pricing 2013 sept 20th by vikram singh sankhala
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
An Introduction to Risk - by Vikram Sankhala
An Introduction to Risk - by Vikram SankhalaAn Introduction to Risk - by Vikram Sankhala
An Introduction to Risk - by Vikram Sankhala
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Transfer Pricing Vikram Sankhala
Transfer Pricing   Vikram SankhalaTransfer Pricing   Vikram Sankhala
Transfer Pricing Vikram Sankhala
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Tax issues in mergers and acquisitions
Tax issues in mergers and acquisitionsTax issues in mergers and acquisitions
Tax issues in mergers and acquisitions
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
LTCM Case
LTCM CaseLTCM Case
Asset Liability Management
Asset Liability ManagementAsset Liability Management
Global financial markets
Global financial marketsGlobal financial markets
Tax presentation business income
Tax presentation   business incomeTax presentation   business income
Tax presentation business income
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Tax planning for salaried individuals
Tax planning for salaried individualsTax planning for salaried individuals
Tax planning for salaried individuals
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Tax presentation salaries part 2
Tax presentation salaries   part 2Tax presentation salaries   part 2
Tax presentation salaries part 2
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 
Tax presentation salaries part i
Tax presentation salaries part iTax presentation salaries part i
Tax presentation salaries part i
Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr
 

More from Vikram Sankhala IIT, IIM, Ex IRS, FRM, Fin.Engr (20)

Primer on major data mining algorithms
Primer on major data mining algorithmsPrimer on major data mining algorithms
Primer on major data mining algorithms
 
Vikram emerging technologies
Vikram emerging technologiesVikram emerging technologies
Vikram emerging technologies
 
Blockchain concept explained
Blockchain concept explainedBlockchain concept explained
Blockchain concept explained
 
Hyperloop explained
Hyperloop explainedHyperloop explained
Hyperloop explained
 
Vikram budget 2018
Vikram budget 2018Vikram budget 2018
Vikram budget 2018
 
Vikram cgst updated budget 2018
Vikram cgst updated budget 2018Vikram cgst updated budget 2018
Vikram cgst updated budget 2018
 
Basic health facts presentation by vikram
Basic health facts presentation  by vikramBasic health facts presentation  by vikram
Basic health facts presentation by vikram
 
Gst simplified vikram sankhala
Gst simplified vikram sankhalaGst simplified vikram sankhala
Gst simplified vikram sankhala
 
Paper -future_of_finance_function
Paper  -future_of_finance_functionPaper  -future_of_finance_function
Paper -future_of_finance_function
 
Transfer pricing 2013 sept 20th by vikram singh sankhala
Transfer pricing 2013 sept 20th by vikram singh sankhalaTransfer pricing 2013 sept 20th by vikram singh sankhala
Transfer pricing 2013 sept 20th by vikram singh sankhala
 
An Introduction to Risk - by Vikram Sankhala
An Introduction to Risk - by Vikram SankhalaAn Introduction to Risk - by Vikram Sankhala
An Introduction to Risk - by Vikram Sankhala
 
Transfer Pricing Vikram Sankhala
Transfer Pricing   Vikram SankhalaTransfer Pricing   Vikram Sankhala
Transfer Pricing Vikram Sankhala
 
Tax issues in mergers and acquisitions
Tax issues in mergers and acquisitionsTax issues in mergers and acquisitions
Tax issues in mergers and acquisitions
 
LTCM Case
LTCM CaseLTCM Case
LTCM Case
 
Asset Liability Management
Asset Liability ManagementAsset Liability Management
Asset Liability Management
 
Global financial markets
Global financial marketsGlobal financial markets
Global financial markets
 
Tax presentation business income
Tax presentation   business incomeTax presentation   business income
Tax presentation business income
 
Tax planning for salaried individuals
Tax planning for salaried individualsTax planning for salaried individuals
Tax planning for salaried individuals
 
Tax presentation salaries part 2
Tax presentation salaries   part 2Tax presentation salaries   part 2
Tax presentation salaries part 2
 
Tax presentation salaries part i
Tax presentation salaries part iTax presentation salaries part i
Tax presentation salaries part i
 

Recently uploaded

Authoring a personal GPT for your research and practice: How we created the Q...
Authoring a personal GPT for your research and practice: How we created the Q...Authoring a personal GPT for your research and practice: How we created the Q...
Authoring a personal GPT for your research and practice: How we created the Q...
Leonel Morgado
 
Medical Orthopedic PowerPoint Templates.pptx
Medical Orthopedic PowerPoint Templates.pptxMedical Orthopedic PowerPoint Templates.pptx
Medical Orthopedic PowerPoint Templates.pptx
terusbelajar5
 
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdfTopic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
TinyAnderson
 
20240520 Planning a Circuit Simulator in JavaScript.pptx
20240520 Planning a Circuit Simulator in JavaScript.pptx20240520 Planning a Circuit Simulator in JavaScript.pptx
20240520 Planning a Circuit Simulator in JavaScript.pptx
Sharon Liu
 
Cytokines and their role in immune regulation.pptx
Cytokines and their role in immune regulation.pptxCytokines and their role in immune regulation.pptx
Cytokines and their role in immune regulation.pptx
Hitesh Sikarwar
 
ESR spectroscopy in liquid food and beverages.pptx
ESR spectroscopy in liquid food and beverages.pptxESR spectroscopy in liquid food and beverages.pptx
ESR spectroscopy in liquid food and beverages.pptx
PRIYANKA PATEL
 
The binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defectsThe binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defects
Sérgio Sacani
 
NuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyerNuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyer
pablovgd
 
8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf
by6843629
 
waterlessdyeingtechnolgyusing carbon dioxide chemicalspdf
waterlessdyeingtechnolgyusing carbon dioxide chemicalspdfwaterlessdyeingtechnolgyusing carbon dioxide chemicalspdf
waterlessdyeingtechnolgyusing carbon dioxide chemicalspdf
LengamoLAppostilic
 
Immersive Learning That Works: Research Grounding and Paths Forward
Immersive Learning That Works: Research Grounding and Paths ForwardImmersive Learning That Works: Research Grounding and Paths Forward
Immersive Learning That Works: Research Grounding and Paths Forward
Leonel Morgado
 
Randomised Optimisation Algorithms in DAPHNE
Randomised Optimisation Algorithms in DAPHNERandomised Optimisation Algorithms in DAPHNE
Randomised Optimisation Algorithms in DAPHNE
University of Maribor
 
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero WaterSharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Texas Alliance of Groundwater Districts
 
Bob Reedy - Nitrate in Texas Groundwater.pdf
Bob Reedy - Nitrate in Texas Groundwater.pdfBob Reedy - Nitrate in Texas Groundwater.pdf
Bob Reedy - Nitrate in Texas Groundwater.pdf
Texas Alliance of Groundwater Districts
 
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốtmô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
HongcNguyn6
 
在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样
在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样
在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样
vluwdy49
 
Basics of crystallography, crystal systems, classes and different forms
Basics of crystallography, crystal systems, classes and different formsBasics of crystallography, crystal systems, classes and different forms
Basics of crystallography, crystal systems, classes and different forms
MaheshaNanjegowda
 
aziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobelaziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobel
İsa Badur
 
Equivariant neural networks and representation theory
Equivariant neural networks and representation theoryEquivariant neural networks and representation theory
Equivariant neural networks and representation theory
Daniel Tubbenhauer
 
bordetella pertussis.................................ppt
bordetella pertussis.................................pptbordetella pertussis.................................ppt
bordetella pertussis.................................ppt
kejapriya1
 

Recently uploaded (20)

Authoring a personal GPT for your research and practice: How we created the Q...
Authoring a personal GPT for your research and practice: How we created the Q...Authoring a personal GPT for your research and practice: How we created the Q...
Authoring a personal GPT for your research and practice: How we created the Q...
 
Medical Orthopedic PowerPoint Templates.pptx
Medical Orthopedic PowerPoint Templates.pptxMedical Orthopedic PowerPoint Templates.pptx
Medical Orthopedic PowerPoint Templates.pptx
 
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdfTopic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
 
20240520 Planning a Circuit Simulator in JavaScript.pptx
20240520 Planning a Circuit Simulator in JavaScript.pptx20240520 Planning a Circuit Simulator in JavaScript.pptx
20240520 Planning a Circuit Simulator in JavaScript.pptx
 
Cytokines and their role in immune regulation.pptx
Cytokines and their role in immune regulation.pptxCytokines and their role in immune regulation.pptx
Cytokines and their role in immune regulation.pptx
 
ESR spectroscopy in liquid food and beverages.pptx
ESR spectroscopy in liquid food and beverages.pptxESR spectroscopy in liquid food and beverages.pptx
ESR spectroscopy in liquid food and beverages.pptx
 
The binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defectsThe binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defects
 
NuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyerNuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyer
 
8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf
 
waterlessdyeingtechnolgyusing carbon dioxide chemicalspdf
waterlessdyeingtechnolgyusing carbon dioxide chemicalspdfwaterlessdyeingtechnolgyusing carbon dioxide chemicalspdf
waterlessdyeingtechnolgyusing carbon dioxide chemicalspdf
 
Immersive Learning That Works: Research Grounding and Paths Forward
Immersive Learning That Works: Research Grounding and Paths ForwardImmersive Learning That Works: Research Grounding and Paths Forward
Immersive Learning That Works: Research Grounding and Paths Forward
 
Randomised Optimisation Algorithms in DAPHNE
Randomised Optimisation Algorithms in DAPHNERandomised Optimisation Algorithms in DAPHNE
Randomised Optimisation Algorithms in DAPHNE
 
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero WaterSharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
 
Bob Reedy - Nitrate in Texas Groundwater.pdf
Bob Reedy - Nitrate in Texas Groundwater.pdfBob Reedy - Nitrate in Texas Groundwater.pdf
Bob Reedy - Nitrate in Texas Groundwater.pdf
 
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốtmô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
 
在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样
在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样
在线办理(salfor毕业证书)索尔福德大学毕业证毕业完成信一模一样
 
Basics of crystallography, crystal systems, classes and different forms
Basics of crystallography, crystal systems, classes and different formsBasics of crystallography, crystal systems, classes and different forms
Basics of crystallography, crystal systems, classes and different forms
 
aziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobelaziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobel
 
Equivariant neural networks and representation theory
Equivariant neural networks and representation theoryEquivariant neural networks and representation theory
Equivariant neural networks and representation theory
 
bordetella pertussis.................................ppt
bordetella pertussis.................................pptbordetella pertussis.................................ppt
bordetella pertussis.................................ppt
 

Non linear dynamical systems

  • 2. ISOLATED SYSTEM • Zero interaction with environment. • In Real World it is difficult to isolate a system from its Environment
  • 3. NON LINEAR SYSTEMS • Multiple Inputs • Feedback Loops • Error grow Exponentially • Sensitivity to Initial Conditions
  • 4. DISTRIBUTED SYSTEMS • Multiple Interacting Non Linear Dynamic Systems as Components
  • 5. MODELLING NON LINEAR DYNAMICAL SYSTEMS • Stochastic noise-driven linear and nonlinear dynamical systems. • Another approach involves a state space where time series observations are transformed to the phase space vectors. They model the dynamics of a system by modeling the dynamics of the corresponding points in the phase space using a Mapping Function • The Mapping Function can be used for Prediction of future states.
  • 6. DIMENSION REDUCTION • Principal Components Analysis – Linear Method • Non Linear Techniques are also there
  • 7. ALGORITHMIC METHODS • As soon as you introduce self-loops in your model structure, you introduce time, and therefore the system becomes dynamical. • In many statistical models, we don't have a closed form solution for inference on particular variables, so we must use iterative/algorithmic methods to approximate / sample values. • Neural Networks play an important role for modelling Dynamic non linear systems.
  • 8. ARTIFICIAL NEURAL NETWORKS • Consist of Connected local processing elements (neurons) • These accept weighted inputs from other such elements • They use these weighted inputs to give a single output
  • 9. FREEMAN 1991 • Artificial neural systems were designed to capture some of the useful brain functions by modeling the features of the brain. • Chaos "may be the chief property that makes the brain different from an artificial- intelligence machine“.
  • 10. CHAOS • Chaos is statistically indistinguishable from randomness, and yet it is deterministic and not random at all. • A chaotic system will produce the same results if given the same inputs • But you can not predict in what way the system's behavior will change for any change in the input to that system • It is random appearing, and yet has a large degree of underlying order.
  • 11. BUTTERFLY EFFECT • Affects Initial Conditions • Initial Condition inaccuracy grows exponentially. • We get extra ordinary and Counter Intuitive Results
  • 12. CHAOS ENGINEERING • How Emergent behavior from Component Interactions can cause the system to devove into Chaotic state, • Controlled Experiments on Distributed Systems by introducing failure.