The literature on chaos has highlighted several chaotic systems with special features. In this work, a novel chaotic jerk system with non-hyperbolic equilibrium is proposed. The dynamics of this new system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, we investigate the time-delay effects on the proposed system. Realisation of such a system is presented to verify its feasibility.

Nowadays, designing chaotic systems with hidden attractor is one of the most interesting topics in nonlinear dynamics and chaos. In this paper, a new 4D chaotic system is proposed. This new chaotic system has no equilibria, and so it belongs to the category of systems with hidden attractors. Dynamical features of this systemare investigated with the help of its state-space portraits, bifurcation diagram, Lyapunov exponents diagram, and basin of attraction. Also a hardware realisation of this system is proposed by using field programmable gate arrays(FPGA). In addition, an electronic circuit design for the chaotic system is introduced.

In this paper, we design a new two-dimensional nonlinear oscillator with infinite number of coexisting limit cycles distributed in a plane. One-third of these limit cycles are self-excited attractors while two-third of them are hidden attractors. Modifying this new system to its forced version, we obtain a new nonlinear system with infinite number of coexisting torus attractors and limit cycle attractors.