A Novel hyperchaotic System with Stable and Unstable Line of Equilibria and Sigma Shaped Poincare Map

The objective of the paper is to develop a novel hyperchaotic system with a line of equilibria and sigma shaped Poincare map. The proposed hyperchaotic system has unstable and stable equilibria based on the values of the state variable. The system is relatively simpler than the reported hyperchaotic systems with a line of equilibria. The proposed system also depicts the chaotic and quasi-periodic behaviours for variation of two bifurcation parameters in parameter space. The proposed system is asymmetrical to its axes, plane and space. The system with above combination of features are rare in the literature and is the novelty of the paper. Bifurcation diagram, Lyapunov spectrum, frequency spectrum and hyperchaotic attractor of the system are presented to validate the different unique behaviours of the system.