Stabilising Unstable Fixed Point and Chaos Control in a Prey–Predator Model with Random Shock

An asymptotic method of stabilisation of unstable fixed point and controlling chaos in 2-D system has been employed to a prey–predator system which is subjected to the application of a random shock. Chaotic and controlled evolutions are observed by drawing bifurcation diagrams, chaotic and regular attractors, time series and phase plots and plots of Lyapunov exponents. For complexity analysis, numerical investigation is extended to obtain correlation dimensions for regular and chaotic motions. The indicator ‘dynamic Lyapunov indicator’ has also been used to confirm above type of evolutions.