Phase Portrait Analysis and Limit Cycles
Consider the dynamical system described by the differential equations: \(\frac{dx}{dt} = x(1-x) – \frac{xy}{1+x}\) \(\frac{dy}{dt} = k\,y\left(\frac{x}{1+x} – d\right)\) where \(x(t)\) and \(y(t)\) represent population densities, and \(k\) and \(d\) are positive parameters with \(0 < d < 1\). Assume parameter values such that a non-linear cycle exists. (a) Find all equilibrium points of the […]