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Initial-switched boosting bifurcations in 2D hyperchaotic map
Chaos: An Interdisciplinary Journal of Nonlinear Science ( IF 2.9 ) Pub Date : 2020-03-02 , DOI: 10.1063/5.0002554
B. C. Bao 1 , H. Z. Li 1 , L. Zhu 2, 3 , X. Zhang 1 , M. Chen 1
Affiliation  

Recently, the coexistence of initial-boosting attractors in continuous-time systems has been attracting more attention. How do you implement the coexistence of initial-boosting attractors in a discrete-time map? To address this issue, this paper proposes a novel two-dimensional (2D) hyperchaotic map with a simple algebraic structure. The 2D hyperchaotic map has two special cases of line and no fixed points. The parameter-dependent and initial-boosting bifurcations for these two cases of line and no fixed points are investigated by employing several numerical methods. The simulated results indicate that complex dynamical behaviors including hyperchaos, chaos, and period are closely related to the control parameter and initial conditions. Particularly, the boosting bifurcations of the 2D hyperchaotic map are switched by one of its initial conditions. The distinct property allows the dynamic amplitudes of hyperchaotic/chaotic sequences to be controlled by switching the initial condition, which is especially suitable for chaos-based engineering applications. Besides, a microcontroller-based hardware platform is developed to confirm the generation of initial-switched boosting hyperchaos/chaos.

中文翻译:

二维超混沌映射中的初始切换的增强分叉

最近,连续时间系统中的初始提升吸引子并存已经引起了更多关注。如何在离散时间图中实现初始提升吸引子的共存?为了解决这个问题,本文提出了一种具有简单代数结构的新型二维(2D)超混沌映射。2D超混沌图具有线的两种特殊情况,没有固定点。通过使用几种数值方法,研究了这两种情况下的参数相关和初始提升的分叉,没有固定点。仿真结果表明,复杂的动力学行为包括超混沌,混沌和周期与控制参数和初始条件密切相关。特别地,通过其初始条件之一来切换2D超混沌映射的增强分叉。独特的属性允许通过切换初始条件来控制超混沌/混沌序列的动态幅度,这特别适用于基于混沌的工程应用。此外,开发了基于微控制器的硬件平台,以确认初始开关升压超混沌/混沌的产生。
更新日期:2020-04-10
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