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

Chaos control of Hastings-Powell model by combining chaotic motions