Chapter 8.4, Problem 10E

Interpretation Introduction

Interpretation:

(a) To plot the nullclines in the phase plane and to study how their intersection changes as detuning of “a” is increased from negative value to large positive value.

(b) To show that the number of stable fixed points increases from $\text{1 to 2}$ and then $\text{1}$ again as “a” increases, by assuming ${\text{b > b}}_{\text{c}}$.

Concept Introduction:

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

Nullclines are the curves where either $\dot{\text{x}}=0\text{ or }\dot{\text{y}}\text{ = 0}$. They show whether the flow is completely vertical or horizontal.

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