A new hyperchaotic system with Hopf bifurcation and its boundedness: infinite coexisting hidden and self-excited attractor

Ayub, Javeria; Aqeel, Muhammad; Sunny, Danish Ali

doi:10.1007/s00500-022-07608-5

Cited by 2 publications

(1 citation statement)

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“…Understanding the behavior of attractors, which characterize the long-run dynamics of these systems, is a crucial aspect of their analysis [3][4][5]. Attractors can be broadly divided into two classes: self-excited attractors, which arise from unstable fixed points [6][7][8], and hidden attractors, which arise in systems with stable fixed points [9][10][11], no equilibrium points [12], or multiple line equilibria [13]. The exploration of hidden attractors has opened up new avenues for deeper insights into and manipulation of the chaotic behavior exhibited by such systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis and circuit realization of a new controllable hyperchaotic system

Lalili,

Bouden,

Grimes

et al. 2024

Phys. Scr.

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Amidst the realm of hyper-chaotic systems, a notable deficiency is the absence of amplitude control and signal polarity. This paper addresses this limitation by introducing a new 4-D hyper-chaotic system with a hidden equilibrium-free attractor. The study focuses on amplitude control, achieved by adjusting a specific parameter, enabling manipulation of variable magnitudes while maintaining the overall signal. The offset boosting technique is investigated, enabling flexible shifting of the attractor in a desired direction. A real circuit experiment validates the proposed system's practical applicability, confirming consistency with theoretical analysis and numerical simulations. Through introducing this new-found, the study holds significant importance for various fields, such as communications engineering and chaos-based cryptography, where precise control of signal characteristics is paramount.

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