A new chaotic jerk system with hidden heart-shaped attractor: dynamical analysis, multistability, connecting curves and its application in image encryption

Application of chaos in modeling natural phenomena and encryption encourages researchers to design new chaotic systems with exciting features. Here a chaotic jerk oscillator with different properties is proposed. Previous studies mainly used non-polynomial and piecewise linear terms to design the attractors' shape. In the paper, the heart-shaped attractor is designed using just polynomial terms. This system is studied by considering its bifurcation diagram, Lyapunov exponent, and basin of attraction. These tools show that the proposed system has chaotic and periodic attractors that coexist in some parameter intervals. The oscillator does not have an equilibrium and has a heart-shaped attractor. Moreover, the connecting curves of the oscillator are considered to explore other structural properties. Numerical results confirm the analytical solutions for the system's connecting curves. The interesting dynamics of the oscillator are used in an encryption and compression application.