Hyperchaos, extreme multistability, and hidden attractors in the novel complex nonlinear system and its adaptive hybrid synchronization

In this paper, a novel hyperchaotic complex nonlinear system is proposed by introducing a simple linear feedback controller and a complex constant to the complex simplified Lorenz system. Dynamics of the complex simplified Lorenz hyperchaotic system is investigated by theoretical analysis and numerical simulation, including Lyapunov exponents, bifurcation diagrams, phase portraits, Poincare section, and basins of attraction. The results show that it has no equilibrium, one equilibrium, and a plane of equilibria for different parameter regions and exhibits rich dynamical characteristics, including hyperchaos, typical bifurcations, extreme multistability, as well as hidden attractors. Moreover, the adaptive hybrid synchronization between two complex simplified Lorenz hyperchaotic systems with unknown parameters is achieved by using the passivity-based adaptive control method. The numerical simulations are worked out to verify the effectiveness and feasibility of the proposed synchronization scheme, thereby laying the foundation for the applications of the complex simplified Lorenz hyperchaotic system.