Chapter 6.6, Problem 9E

Interpretation Introduction

Interpretation:

To show that array of Josephson junctions is the reversible system for phase difference ${\text{θ}}_{\text{k}}$, to show that there are four fixed points when $\left|\frac{\Omega }{(a+1)}\right|<1$, and none when $\left|\frac{\Omega }{(a+1)}\right|>1$, also to generate various phase portraits for a = 1 and varying values of $\Omega$ in interval [1,3].

Concept Introduction:

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

The Josephson junction is the superconducting device that generates high-frequency voltage oscillations. The junction consists of the two closely spaced conductors that are separated by the weak connection.

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.