A Systematic Methodology for Constructing Hyperchaotic Systems With Multiple Positive Lyapunov Exponents and Circuit Implementation

Dynamics analysis and robust modified function projective synchronization of Sprott E system with quadratic perturbation

“…Moreover, in future works, we will use the proposed analysis method to investigate some complex chaotic systems, such as the typical multi-scroll chaotic systems [18] by some effective design methods using trigonometric functions, cellular neural networks, nonlinear modulating functions etc and the networked chaotic systems [3 -5]. It is expected that more detailed theory analysis will be provided in a forthcoming paper.…”

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

“…A numerical simulation is conducted to illustrate the validity and feasibility of the proposed adaptive controllers and parameter update laws. Recently, many researchers have begun to give their attention to the multiscroll chaotic systems [28] and the networked chaotic systems [3] - [5]. Consequently, we will investigate the SMFPS of these systems in our future work.…”

A Sinusoidally Driven Lorenz System and Circuit Implementation

“…According to Cardan discriminant Δ = ( /2) 2 + ( /3) 3 , when Δ > 0, there exist a real root and two complex roots in (5). Since the equilibrium points cannot be complex numbers, this means that the system does not have equilibrium points since Δ > 0.…”

“…In 1979, Rössler found the first chaotic system with two positive Lyapunov exponents, referred to as the Rössler hyperchaotic system [2]. Comparing with a chaotic attractor with one positive Lyapunov exponent, the hyperchaotic attractor expands in two or more directions simultaneously [3][4][5]. It means that the hyperchaotic attractor has much more complex topological structure and therefore has much better performances in many real-world applications such as secure communication and encryption.…”