Crisis and inverse crisis route to chaos in a new 3-D chaotic system with saddle, saddle foci and stable node foci nature of equilibria

This paper reports a new 3-D autonomous chaotic system with novel behaviour. The proposed system has three different natures of equilibria: (i) saddle, (ii) saddle foci and (iii) stable node foci which is new in the literature. The system has invariant nature of the equilibria in the considered ranges of all five bifurcation parameters. The system has various complex dynamic behaviours like periodic (period-1, period-2, period-4), quasi-periodic, chaotic transient, stable and chaotic attractor. The system exhibits (i) inverse crises route to chaos for two bifurcation parameters and (ii) crises route to chaos for another three bifurcation parameters. It is observed that in case of normal parameter ranges, the trajectories of the system are concentrated only near an unstable equilibrium point, but in the transient chaotic parameters ranges the trajectories of the system switchover to a stable equilibrium point from the unstable equilibrium point. The transient chaotic nature of the system is analysed using the many numerical tools like Lyapunov exponents, instantaneous phase, Poincare return map, recurrence plot, 0-1 test analysis, autocorrelation plot. The findings of the numerical tools are validated using the circuit implementation.