A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium

Abstract

A new hyper-chaotic system is presented in this paper by adding a smooth flux-controlled memristor and a cross-product item into a three-dimensional autonomous chaotic system. It is exciting that this new memristive system can show a four-wing hyperchaotic attractor with a line equilibrium. The dynamical behaviors of the proposed system are analyzed by Lyapunov exponents, bifurcation diagram and Poincaré maps. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of hyperchaos in the system is verified theoretically. Finally, an electronic circuit is designed to implement the hyperchaotic memristive system.

An Improved Memristive Diode Bridge-Based Band Pass Filter Chaotic Circuit

“…Due to the unique nonlinear characteristics of memristors [1], an explosive growth study of memristor based circuits has been boosted up in the past years [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Unfortunately, induced by technical handicaps in fabricating nanoscale memristor, the commercial memristor is not expected to be available in the near future.…”

“…Unfortunately, induced by technical handicaps in fabricating nanoscale memristor, the commercial memristor is not expected to be available in the near future. Thus, various kinds of physically implementable equivalent circuits which can manifest the three fingerprints of memristors [17] have attracted much attention [2,[6][7][8][9][10][11][12][13][14][15][16][17][18]. Popularly, the circuits implemented by operational amplifiers and analog multipliers [7][8][9][10][11][12] as well as the circuits consisting of diode bridge cascaded with RC [13][14][15], LC [16], and RLC [18] filters have been used for experimental measurements in memristor based circuits.…”

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

“…By replacing Chua's diodes with memristors, adding memristors to existing nonlinear systems, and designing new systems with memristors, some new chaotic and hyperchaotic systems have been constructed, such as a memristor-based Chua's circuit [1][2][3][4][5][6], memristor-based van der Pol oscillator [7], memristor-based Lorenz system [8][9][10], memristor-based Chen system [11], memristor-based Lü system [12], etc. Theoretical analyses, numerical simulations and circuit experiments consistently indicate that such memristor-based systems can exhibit complex dynamical behaviours including various bifurcation [1][2][3][4][5][6][7][8][9][10][11][12], chaos [1][2][3][4][5][6][7][8][9][10][11][12], hyperchaos [12][13][14], coexistence of attractors [15], transient dynamical behaviors [16], and initial state dependent dynamical behaviors [17]. Moreover, several fractional-order memristor-based systems and their dynamical behaviors are presented in [9,…”

Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System

“…However, a lot of literature with respect to the memristive chaotic system applied to secure communication only extracted its own chaotic sequence, without involving the memristive synchronization scheme [12,19,20]. In addition, the multiwings [21,22] and multistability [23,24] of memristive chaotic systems have been a hot topic. Nevertheless, there were few studies on the multiwing memristive circuit based on Lorenz system, and less literature took the fact that the multistability may produce different encryption effects into consideration.…”