Minkowski semi-planes

Rinaldi, Gloria

doi:10.1007/bf01222271

Cited by 2 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since their nonlinear multi-trophic model was introduced, theoretical ecologists started to analyze the subtle dynamics of these kind of systems (see e.g. [19,33,28,20] or [43], which is an accessible mathematical introduction of complex dynamics with many biological examples).…”

Section: Introductionmentioning

confidence: 99%

Chaos control of Hastings–Powell model by combining chaotic motions

Danca

Chattopadhyay

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

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.

show abstract