TY - JOUR

T1 - Rich dynamics and anticontrol of extinction in a prey–predator system

AU - Danca, Marius F.

AU - Fečkan, Michal

AU - Kuznetsov, Nikolay

AU - Chen, Guanrong

PY - 2019/10/1

Y1 - 2019/10/1

N2 - This paper reveals some new and rich dynamics of a two-dimensional prey–predator system and to anticontrol the extinction of one of the species. For a particular value of the bifurcation parameter, one of the system variable dynamics is going to extinct, while another remains chaotic. To prevent the extinction, a simple anticontrol algorithm is applied so that the system or bits can escape from the vanishing trap. As the bifurcation parameter increases, the system presents quasiperiodic, stable, chaotic and also hyperchaotic orbits. Some of the chaotic attractors are Kaplan–Yorke type, in the sense that the sum of its Lyapunov exponents is positive. Also, atypically for undriven discrete systems, it is numerically found that, for some small parameter ranges, the system seemingly presents strange nonchaotic attractors. It is shown both analytically and by numerical simulations that the original system and the anticontrolled system undergo several Neimark–Sacker bifurcations. Beside the classical numerical tools for analyzing chaotic systems, such as phase portraits, time series and power spectral density, the ‘0–1’ test is used to differentiate regular attractors from chaotic attractors.

AB - This paper reveals some new and rich dynamics of a two-dimensional prey–predator system and to anticontrol the extinction of one of the species. For a particular value of the bifurcation parameter, one of the system variable dynamics is going to extinct, while another remains chaotic. To prevent the extinction, a simple anticontrol algorithm is applied so that the system or bits can escape from the vanishing trap. As the bifurcation parameter increases, the system presents quasiperiodic, stable, chaotic and also hyperchaotic orbits. Some of the chaotic attractors are Kaplan–Yorke type, in the sense that the sum of its Lyapunov exponents is positive. Also, atypically for undriven discrete systems, it is numerically found that, for some small parameter ranges, the system seemingly presents strange nonchaotic attractors. It is shown both analytically and by numerical simulations that the original system and the anticontrolled system undergo several Neimark–Sacker bifurcations. Beside the classical numerical tools for analyzing chaotic systems, such as phase portraits, time series and power spectral density, the ‘0–1’ test is used to differentiate regular attractors from chaotic attractors.

KW - Anticontrol

KW - Neimark–Sacker bifurcation

KW - Prey–predator system

KW - Strange nonchaotic attractor

KW - ‘0–1’ test

UR - http://www.scopus.com/inward/record.url?scp=85073681599&partnerID=8YFLogxK

U2 - 10.1007/s11071-019-05272-3

DO - 10.1007/s11071-019-05272-3

M3 - Article

AN - SCOPUS:85073681599

VL - 98

SP - 1421

EP - 1445

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 2

ER -