Multiple Alternatives of Offset Boosting in a Symmetric Hyperchaotic Map

Abstract

The offset as the average value of a variable plays an important role in signal processing and system design. Offset boosting can be realized by a non-bifurcation parameter or an initial condition. In this work, symmetric coexisting attractors with opposite polarity and a 2D hyperchaotic map with multiple modes of offset boosting are proposed, where the offset can be controlled both by the initial condition and system parameter, and as a result, multiple alternatives of offset boosting and offset competition show up. Consequently, the final offset is determined eventually by the balance of two factors. The theoretical findings are verified through the hardware experiment based on the STM32. Finally, a pseudo-random number generator (PRNG) is constructed based on the newly proposed hyperchaotic map, demonstrating its high performance in engineering applications.

Robust multiple-scroll dynamics in memristive-based generator system

“…So far, it has been confirmed that some hyperchaotic systems that exhibit multi-scroll and multi-wing behaviors have also been proven to carry more complexity than those with few attractors 26 . These new findings will play a major role and robust application in image encryption 26 , memristors 27 , and secure communication devices 28 . Very recently, Jafari et al 26 proposed a 2 by 3 grid multi-scroll and multi-wing attractors with hidden attractors from 3D-system without equilibrium by simple state variable modification to the original Sprott-A system.…”

“…Very recently, Jafari et al 26 proposed a 2 by 3 grid multi-scroll and multi-wing attractors with hidden attractors from 3D-system without equilibrium by simple state variable modification to the original Sprott-A system. Hu et al 29 also discovered a multi-scroll chaotic sea in a simple sine function nonlinear 3D Sprott-A system, while a numerical and experimental validation of an improved Jerk hyperchaotic multi-scroll system has been reported with infinite number of equilibrium 28 . Systems without equilibrium, hidden attractors that exhibits multi-scroll and multi-wings has also been discovered in the Lorenz-like system with a designed saw tooth wave function 4D system using a state feedback controller 30 .…”

“…In this regard, an hyperchaotic system is defined as a chaotic system with at least two positive Lyapunov exponents, high sensitivity to initial conditions, more randomness, higher unpredictability and at least four dimensional phase space. Obviously, hyperchaotic systems have wide applications and therefore more preferred than the chaotic systems in recent central topic researches including synchronization 2 , neural networks 3 , finance 4 , nonlinear circuits 2 – 5 , chaos-based secure communication 28 among others. Such systems exhibits multi-scroll and multi-wings attractors and therefore played a vital role in engineering and technology applications 6 – 8 .…”

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.…”

Autonomous piecewise damping Josephson junction jerk oscillator: microcontroller implementation, controls, and combination synchronization

“…In the recent literature, Kingni et al [52] exposed an autonomous 5D complex system with offsetboosting controls. Furthermore, considering a symmetric hyperchaotic model, Ge et al [53] put on view multiple possible offset-boosting controls. Exploration of two techniques in achieving offset boosting control in complex models which are the parameter introducing technique and the method of absolute value or periodic functions was reported by Li et al [48].…”