On Autonomous and Nonautonomous Modified Hyperchaotic Complex Lü Systems

Abstract

In this paper autonomous and nonautonomous modified hyperchaotic complex Lü systems are proposed. Our systems have been generated by using state feedback and complex periodic forcing. The basic properties of these systems are studied. Parameters range for hyperchaotic attractors to exist are calculated. These systems have very rich dynamics in a wide range of parameters. The analytical results are tested numerically and excellent agreement is found. A circuit diagram is designed for one of these hyperchaotic complex systems and simulated using Matlab/Simulink to verify the hyperchaotic behavior.

Synchronization of a Novel Hyperchaotic Complex-Variable System Based on Finite-Time Stability Theory

“…Example 1. Consider strategy 1 with the controllers given by Equation (11). We choose L 1 = 3, L 2 = 3 and k = 7/9, Figures 1 and 2 show the results of numerical simulation.…”

“…Figure 1. The states of the drive system in Equation (6) and the response system in Equation (7) with controllers given by Equation (11). Example 2.…”

“…Since Fowler et al [6] generalized the real Lorenz model to a complex Lorenz model, which can be used to describe and simulate the physics of a detuned laser and the thermal convection of liquid flows [7,8], complex chaotic and hyperchaotic systems have been intensively studied. After the complex Lorenz model, many other chaotic and hyperchaotic complex-variable systems have been reported, including the complex Chen and complex Lü systems [9], complex detuned laser system [10], complex modified hyperchaotic Lü system [11], and a novel hyperchaotic complex-variable system [12] which generates 2-, 3-and 4-scroll attractors.…”

Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification

“…The authors [23] constructed a complex nonlinear hyperchaotic system by adding a cross-product nonlinear term to the complex Lorenz system. A complex modified hyperchaotic Lü system [24] were proposed by introducing complex variables to its real counterpart.…”

Combination Synchronization of Three Identical or Different Nonlinear Complex Hyperchaotic Systems

“…The authors [8] constructed a complex nonlinear hyperchaotic system by adding a cross-product nonlinear term to the complex Lorenz system. A complex modified hyperchaotic Lü system [9] was proposed by introducing complex variables to its real counterpart.…”