Dynamic Analysis and Projective Synchronization of a New 4D System

A new 4D dissipative hyperchaotic system with an unstable equilibrium point is introduced. The proposed system consists of ten terms including three quadratic nonlinearities which constructed through using a nonlinear state control algorithm in the known Lorenz system, exhibits self-excited attractors and chaotic system attractors, with two positive derivations of Lyapunov. The dynamical properties of this system are analyzed using theoretical and numerical simulations based on equilibrium points, stability, dissipative, Lyapunov exponents, and phase portrait. Besides, various coexisting attractors or multistability with different initial conditions under the same parameters are investigated. Furthermore, Projective Synchronization (PS) of an identical proposed system is realized by nonlinear control strategy and Lyapunov stability theory.