Modeling of Economic Dynamics https://ek.biem.sumdu.edu.ua/

1. Linear dynamic systems with
continuous time. Equilibrium and
stability of dynamic systems
Senior lecturer, PhD
Iryna Didenko
i.didenko@biem.sumdu.edu.ua

2. 1. Qualitative changes in socio-economic
systems.
2. Qualitative methods of analyzing the
behavior of dynamic systems.
3. Examples of dynamic models.

3. Qualitative changes in socio-
economic systems
Quality characterizes the integral undissected
certainty of objects and phenomena. Any object
has many properties. We perceive and know
only a small part of them.
Structure is a category that characterizes
distribution and interaction in the space of
elements, objects and phenomena, the program of
their development. Changing the quality of items
in all cases is associated with restructuring
structures of their elements.

4. Qualitative changes in socio-
economic systems
Quantitative changes are the increase or decrease of
components some whole, expressed by increasing or
decreasing them quantitative values, which lead at certain
stages of their change to a qualitative leap (the law of
transition from quantitative to qualitative changes).
Structural changes are changes in the ratio of
components, which do not necessarily have to be
accompanied by an increase or decrease in their number. On
the contrary, the number of components may remain
unchanged. Meanwhile, structural changes can also lead to a
qualitative leap. Therefore, we can assume that both
quantitative and structural changes play a causal role in
qualitative changes.

5. Types of qualitative changes in the
system
• due to the quantitative addition of matter
and energy as a result of interaction with
the external environment;
• ss a result of redistribution (without disturbing
the balance) of energy and matter within the
system itself;
• ss a result of changes in the quality of
subsystems (elements) that define the
structure of the system.

6. Phase schedule of sales

7. Sales growth curve over time

8. Characteristics of the stability of
equilibrium states

9. Mobilization model

10. Mobilization model
1. part of the population dropped out (for
various reasons); this value is proportional to the
share of the mobilized population at time tn = n,
ie it will be equal to βMn, where β is the
coefficient of disposal, which is constant for a given
region, β>= 0;
2. the change in the level of mobilization per
unit time is determined by the difference
between the additionally agitated and the retired
population:

11. Mobilization model

12. Model of the arms race
Denote by X = X (t) the armament costs of
country X, and by Y =Y(t) the arms costs of
country Y.

13. Predator-prey model
Let's see how the populations of so-called
predators and victims can change over time
(wolf - hare, pike - crucian).

14. Predator-prey model

15. IW2. Якісний аналіз динамічних
систем в середовищі MathCad
Qualitative analysis of dynamic systems in the
MathCad environment.