A new hyperchaotic Lorenz‐type system: Generation, analysis, and implementation

Abstract

SUMMARYA new four-dimensional continuous-time autonomous hyperchaotic Lorenz-type system is introduced and analyzed. This hyperchaotic system is not only visualized by computer simulation but also verified with bifurcation analysis and realized with an electronic circuit. Moreover, explicit formulae for estimating the ultimate bound and positive invariant set of the system are derived by constructing a family of generalized Lyapunov functions. The findings and results of this paper have good potential in control and synchronization of hyperchaos and their engineering applications.

Generalized complex projective synchronization of chaotic complex systems with unknown parameters

“…We used MATLAB20 11 a for the simu lation and step size was 0.005 s. We used ode4 solver to solve the ordinary differential equation. We assumed that the drive system as a complex Chen system [15], which is 3rd order, and response system as a hyperchaotic complex Lorentz type system [16], which is 4th order. The nonlinear equations of drive system and response system are defined as follows: Hyperchaotic complex Lorentz-type system: …”

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

“…Recently, Li et al [45] proposed a new hyperchaotic Lorenz-type system described by and its attractor is shown in Figure 1. Lately, Dadras et al [46] reported the following four-wing hyperchaotic system, which has only one unstable equilibrium…”

“…When a = 8, b = 40 and r = 14.9, and with the initial condition [10,1,10,1] T , system (5) is hyperchaotic and its attractor is shown in Figure 2. For more information on the dynamical behaviors of these two systems, please refer to [45,46].…”

A Research on Active Control to Synchronize a New 3D Chaotic System

“…The ever present demand for secure communication is one of the foremost form of motivation for studying chaos synchronization [4][5][6]. Various linear and nonlinear control techniques have been developed to carry out synchronization behavior.…”