Rich dynamics and anticontrol of extinction in a prey-predator system

Marius.-F. Danca, Michal Feckan, Nikolay Kuznetsov, Guanrong Chen

Full text: http://dx.doi.org/10.1007/s11071-019-05272-3

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Abstract

This paper reveals some new and rich dynamics of a two-dimensional prey-predatorsystem and to anticontrol the extinction of one of the species. For a particular value of thebifurcation parameter, one of the system variable dynamics is going to extinct, while an-other remains chaotic. To prevent the extinction, a simple anticontrol algorithm is appliedso that the system orbits can escape from the vanishing trap. As the bifurcation param-eter increases, the system presents quasiperiodic, stable, chaotic and also hyperchaoticorbits. Some of the chaotic attractors are Kaplan-Yorke type, in the sense that the sumof its Lyapunov exponents is positive. Also, atypically for undriven discrete systems, it isnumerically found that, for some small parameter ranges, the system seemingly presentsstrange nonchaotic attractors. It is shown both analytically and by numerical simulationsthat the original system and the anticontrolled system undergo several Neimark-Sackerbifurcations. Beside the classical numerical tools for analyzing chaotic systems, such asphase portraits, time series and power spectral density, the '0-1' test is used to differenti-ate regular attractors from chaotic attractors

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