Consider a system of differential equations of the form \( \dot{X}=F(X) \) where \( X \in \mathbb{R}^n \) and \( F \) is a smooth vector valued function. \(X^* \in \mathbb{R}^n \) is called a fixed point if \( F(X^*) = \vec{0} \)
In Chua circuit, we encounter fixed points depending on the value of \(R\)
Let \((X^*,Y^*,Z^*)\) denote a fixed point. Then, the fixed points can be computed as follows:
\(Y^*=0 \hspace{1cm} Z^*=-X^* \hspace{1cm} -X^*=\tilde{g}(X) \)
Recall that the dimensionless form of the non-linear part i.e, \(\tilde{g}(X)\) depended on the value of parameter \(R\). This was due to the fact that the slopes \(\tilde{m_s}\) where \(s \in \{0,1,2\}\) were non-dimensionalized by multiplying \(m_s\) by \(R\). Thus the fixed points depend on the value of \(R\) and can be visualized as the points of intersection of the graphs \( f(x) = -X \) and \(g(x)\).