Chaos control of Hastings–Powell model by combining chaotic motions

Abstract

In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings-Powell (HP) system. The PS algorithm is a convergent scheme that switches the control parameter within a set of values while the controlled system is numerically integrated. The attractor obtained with the PS algorithm matches the attractor obtained by integrating the system with the parameter replaced by the averaged value of the switched parameter values. The switching rule can be applied periodically or randomly over a set of given values. In this way, every stable cycle of the HP system can be approximated if its underlying parameter value equalizes the average value of the switching values. Moreover, the PS algorithm can be viewed as a generalization of Parrondo's game, which is applied for the first time to the HP system, by showing that losing strategy can win: "losing + losing = winning." If "loosing" is replaced with "chaos" and, "winning" with "order" (as the opposite to "chaos"), then by switching the parameter value in the HP system within two values, which generate chaotic motions, the PS algorithm can approximate a stable cycle so that symbolically one can write "chaos + chaos = regular." Also, by considering a different parameter control, new complex dynamics of the HP model are revealed.

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“…The algorithm can be used both for theoretical studies of dynamical systems modeled such as synchronization [21], chaos control and anticontrol, or as generalization of the Parrondo paradox (see e.g. [22,23]), or experimentally as well, like the implementation on real systems, e.g., electronic circuits [24].…”

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“…[30] Parrondo's paradox was first conceptualized as an abstraction of flashing Brownian ratchets, [31][32][33] wherein diffusive particles exhibit unexpected drift when exposed to alternating periodic potentials. It has since been applied across a wide range of disciplines in the physical sciences and engineering-related fields, [34,35] such as diffusive and granular flow dynamics, [36,37] information thermodynamics, [38][39][40] chaos theory, [41][42][43][44][45][46][47] switching problems, [48][49][50] and quantum phenomena. [51][52][53][54][55][56][57] The paradox has also found numerous applications in life science, [58][59][60][61][62] ecology and evolutionary biology, [63][64][65] social dynamics, [66][67][68][69][70] and interdisciplinary work.…”

Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System

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