Chaos control of Hastings-Powell model by combining chaotic motions
Marius-F. Danca, Joydev Chattopadhyay
TL;DR
This paper introduces a Parameter Switching algorithm to control chaos in the Hastings-Powell model, enabling the approximation of stable cycles and revealing new complex dynamics through parameter manipulation.
Contribution
The paper presents a novel chaos control method using parameter switching, applied to the Hastings-Powell system, and demonstrates its effectiveness in stabilizing cycles and exploring complex dynamics.
Findings
The PS algorithm can approximate stable cycles by switching parameters.
Switching chaotic parameters can lead to regular, stable behaviors.
New complex dynamics of the HP model are uncovered through parameter control.
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 +…
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