Chapter 8.6, Problem 4E

Interpretation Introduction

Interpretation:

• (a) To find and classify all the fixed points of the given system.

• (b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions.

• (c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created.

Concept Introduction:

• ➢ The fixed point of a differential equation is the point where $\text{f(x*) = 0 ; while substitution f(x*) = }\dot{\text{x}}\text{ is used and x\&*\#x00A0;is a fixed point}$.

• ➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.