Analytical and numerical study of Hopf bifurcation scenario for a three-dimensional chaotic system

In this article, Hopf bifurcation is characterized for newly proposed Bhalekar–Gejji three-dimensional chaotic dynamical system. By analytical method, a sufficient condition is established for the existence of Hopf bifurcation. Using numerical continuation technique, Hopf bifurcation diagram is analyzed for chaotic parameter which strengthens our analytical results. Moreover, influence of system parameters on dynamical behavior is investigated using phase portraits, Lyapunov exponents, Lyapunov dimensions and Poincaré maps. Theoretical analysis and numerical simulations demonstrate the rich dynamics of the system.