Fuzzy modeling is well-suited for transforming verbal descriptions of biological systems into mathematical models, making it useful for biomimicry. The document discusses how fuzzy modeling has been used to model animal behaviors like territorial fish and light-orienting planarian worms based on descriptions in scientific literature. Fuzzy modeling represents knowledge through an initial description, fuzzy rulebase, and mathematical model, providing interpretability and a means to verify the original description.

1. Biomimicry and Fuzzy Modeling: A Match Made in Heaven Michael Margaliot School of Electrical Engineering Tel Aviv University, Israel SCIS&ISIS’08, Nagoya University, Japan, Sep. 2008.

3. Biomimicry Definition : Biomimicry is the development of artificial products or machines that mimic (or are inspired by) biological phenomena.

4. Motivation for Biomimcry Living systems developed efficient solutions to various problems they encounter in their natural habitat. For example, foraging animals learned how to address the challenge of efficiently navigating and searching in an unknown terrain.

5. Motivation for Biomimicry Scientists are interested in many problems that living systems address. For example: navigation in an unknown terrain is a major challenge in the design of autonomous robots. A natural idea is to follow the solutions already developed by living systems.

6. Examples of Biomimicry Biological Agent foraging animals insects evolution trees immune system social insects Artificial Design autonomous robots walking robots genetic algorithm artificial structures computer security clustering algorithms

7. Biomimcry & Fuzzy Modeling Biomimcry requires “reverse engineering.” In many cases, biologists have already provided a verbal description and explanation of the relevant biological behavior. This reduces biomimicry to the following problem. Problem 1 Transform a given verbal description into a mathematical model or algorithm.

8. Problem 1 & Fuzzy Modeling Extensive research suggests that fuzzy modeling is the most suitable tool for addressing Problem 1. verbal description Fuzzy modeling process: mathematical model fuzzy rule-base simulation/analysis

11. Fuzzy Modeling of Animal Behavior 5. Population dynamics in flies (Rashkovsky & Margaliot, 2007). 6. The Lambda switch (Laschov & Margaliot, 2008).

13. " a real stickleback fight can be seen only when two males are kept together in a large tank where they are both building their nests. The fighting inclinations of a stickleback, at any given moment, are in direct proportion to his proximity to his nest… The vanquished fish invariably flees homeward and the victor chases the other furiously, far into its domain. The farther the victor goes from home, the more his courage ebbs, while that of the vanquished rises in proportion. Arrived in the precincts of his nest, the fugitive gains new strength, turns right about and dashes with gathering fury at his pursuer.” (King Solomon’s Ring, p. 44)

14. Fuzzy Modelling • • • • c 1 x 1 x 2 c 2 If If If If Then Then Then Then and and State variables: Fuzzy rule-base:

15. Inferencing yields the mathematical model: Fuzzy Modelling

18. Orientation to Light in the Dendrocoleum lacteum dim light bright light After a couple of hours:

19. Rate of Change of Direction (r.c.d)

20. r.c.d. and Light Intensity adaptation

22. The “Average Animal”* light Increases  r.c.d increases  AB short adaptation  r.c.d. decreases  CD long (* Fraenkel & Gunn. The Orientation of Animals , 1961) dim light bright light A B C D

23. Fuzzy Modeling L(t) – light intensity A(t) – level of adaptation to light R(t) – r.c.d. B – basal r.c.d. If (L(t)-A(t)) is positive then If (L(t)-A(t)) is negative then If (R(t)-B) is large then If (L(t)-A(t)) is high then Fuzzy rule-base:

24. Fuzzy Modeling

25. Simulation 1 R(t) as a function of time. Light is switched on at t=1.

26. Simulation 2 Trajectory (x(t),y(t)). Light intensity is L(x,y)=x

28. Advantage 1: Interpretability A fuzzy model is interpretable; each parameter has a perceivable meaning. Example 1 : Consider the parameter in the stickleback model. Recall: As decreases, the Gaussian becomes more centered, so Fish becomes “less aggressive.”

29. Advantage 1: Interpretability This links the parameter with the verbal description. The equilibrium points of the mathematical model are: If the equilibrium position is no longer symmetric; eventually fish 1 will have a larger territory than fish 2.

32. Advantage 2: Verification The mathematical model can be examined using both simulations and rigorous analysis. This can be used, to some extent, to verify the original verbal description.

33. Advantage 2: Verification Example : The planarian model includes the rule: If is high, then Consider the case The r.c.d. will not increase, and we may expect that the model’s behavior will change substantially.

34. Advantage 2: Verification For the mathematical model yields: If Recall that the right-hand turns take place at times such that: then so Hence, a periodic trajectory without gradually moving to the shadier parts.

36. Fuzzy Modeling and Animal Behavior 2. Verbal (and therefore vague) information: “ Nor shall I here discuss the various definitions which have been given of the term species . No one definition has as yet satisfied all naturalists; yet every naturalist knows vaguely what he means when he speaks of a species.” (Darwin, 1859) “ A high degree of contact causes low activity.” (Fraenkel & Gunn, 1961)