Two-variable boosting bifurcation in a hyperchaotic map and its hardware implementation

Abstract

There are few reports on the nondestructive adjustment of the oscillation amplitude of the chaotic sequence in the discrete map. To study the lossless regulation of the oscillation amplitude of chaotic sequences, this article proposes a new simple two-dimensional (2D) hyperchaotic map with trigonometric functions. It not only exhibits contains the offset boosting bifurcation and offset boosting coexistence attractors, but also realizes the offset boosting of two state variables with respect to arbitrary parameters in the 2D map. The simulation results of bifurcation diagram, maximum Lyapunov exponent and attractor phase diagram show that the map can produce complex dynamical behaviors. In addition, the introduction of new control parameters into the 2D hyperchaotic chaotic map can also make the hyperchaotic map exhibit rich multistable phenomena. At the same time, the common change of the initial state and the control parameters can realize the arbitrary switching and co-existence of the attractor in the phase plane. In the end, the 2D hyperchaotic map was tested and verified by hardware experiment platform.

Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

“…[1][2][3][4][5][6][7][8][9][10] In general, a system with one positive Lyapunov exponent (LE) is called a chaotic system and a chaotic system with at least two Lyapunov exponents (LEs) greater than zero is called a hyperchaotic system. [11][12][13] Hyperchaos belongs to a kind of chaos but since hyperchaotic systems have at least two positive LEs, their dynamical behavior folds and expands in more directions, and the dynamic properties of hyperchaotic systems are more complex than those of chaotic systems. Therefore, they have a wider prospect for application.…”

A 5-D memristive hyperchaotic system with extreme multistability and its application in image encryption

“…This technology has provided a new approach to researching the control of nonlinear systems in chaotic systems through Offset Boosting control. Subsequently, research on Offset Boosting in chaotic systems has been continuously advancing, with a special focus on aspects such as self-replication of attractors [33], doubling [32], and conditional symmetry [30,34].Subsequently, Ma et al [10]introduced a parameter into the state variables of a four-dimensional dissipative chaotic system with multiple asymmetric attractors and observed state-variable offset boosting in this system. Wang et al [33], in a simple twodimensional hyperchaotic map, introduced trigonometric functions and discovered two types of offset boosting.…”

“…Subsequently, research on Offset Boosting in chaotic systems has been continuously advancing, with a special focus on aspects such as self-replication of attractors [33], doubling [32], and conditional symmetry [30,34].Subsequently, Ma et al [10]introduced a parameter into the state variables of a four-dimensional dissipative chaotic system with multiple asymmetric attractors and observed state-variable offset boosting in this system. Wang et al [33], in a simple twodimensional hyperchaotic map, introduced trigonometric functions and discovered two types of offset boosting. Offset boosting provides the capability to control the amplitude of chaotic systems, which has significant implications for engineering applications.…”

Multistability and Phase Synchronization of Rulkov Neurons Coupled with a Locally Active Discrete Memristor

“…Recently, researchers have shifted their focus to discrete memristors. Introducing discrete memristors to different maps, it was found that discrete memristive chaotic systems have the advantages of high complexity [49][50][51], coexisting attractors [52][53][54], and offset boosting [55]. Furthermore, Peng et al [56] also studied parameter identification for discrete memristive chaotic maps.…”