To analyse the Japanese tree frog system and: (a) To write the system in terms of the phase differences. (b) To show that the experimental result is consistent with the interaction function H(x) = a sin(x) , but this cannot account for the three frog system. (c) To show that the more complicated form of the interaction function H(x) = a sin(x)+ b sin(2x) is obeyed by the three frog system. To plot the phase portraits of the three frog system in terms of the phase differences and explain the experimental results in two or three systems for the various parameter values. (e) To show that adding a small, even periodic component to H does not alter the result qualitatively. Concept Introduction: ➢ The fixed point of a differential equation is the point where, f(x) = 0 ; while substitution f(x) = x ˙ is used and x&*#x00A0;is a fixed point . ➢ The phase portraits represent the trajectories of the system with respect to the parameters and give a qualitative idea about the evolution of the system, its fixed points, whether they will attract or repel the flow, etc.

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Chapter 8.6, Problem 9E

Interpretation Introduction

Interpretation:

To analyse the Japanese tree frog system and:

(a) To write the system in terms of the phase differences.

(b) To show that the experimental result is consistent with the interaction function H(x)= a sin(x), but this cannot account for the three frog system.

(c) To show that the more complicated form of the interaction function H(x)= a sin(x)+ b sin(2x) is obeyed by the three frog system.

To plot the phase portraits of the three frog system in terms of the phase differences and explain the experimental results in two or three systems for the various parameter values.

(e) To show that adding a small, even periodic component to H does not alter the result qualitatively.

Concept Introduction:

➢ The fixed point of a differential equation is the point where, f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point.

➢ The phase portraits represent the trajectories of the system with respect to the parameters and give a qualitative idea about the evolution of the system, its fixed points, whether they will attract or repel the flow, etc.

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