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Abstract:
This paper shows some examples of chaotic systems for the six types of only one hyperbolic equilibrium in changed chameleon-like chaotic system. Two of the six cases have hidden attractors. By adjusting the parameters in the system and controlling the stability of only one equilibrium, we can further obtain chaos with four kinds of conditions: (1) index-0 node; (2) index-3 node; (3) index-0 node foci; (4) index-3 node foci. Based on the method of focus quantities, we study three limit cycles (the outmost and inner cycles are stable, and the intermediate cycle is unstable) bifurcating from an isolated Hopf equilibrium. In addition, one periodic solution can be obtained from a nonisolated zero-Hopf equilibrium. The system may help us in better understanding, revealing an intrinsic relationship of the global dynamical behaviors with the stability of equilibrium point, especially hidden chaotic attractors.
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Source :
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN: 0218-1274
Year: 2019
Issue: 7
Volume: 29
2 . 2 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
ESI HC Threshold:54
JCR Journal Grade:2
Cited Count:
WoS CC Cited Count: 38
SCOPUS Cited Count: 42
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 15
Affiliated Colleges: