Dynamics at infinity, degenerate Hopf and zero-Hopf bifurcation for Kingni–Jafari system with hidden attractors
To understand the complex dynamics of Kingni-Jafari system with hidden attractors, the first objective of this paper was to study the global dynamics, and give a complete description of the dynamics of Kingni-Jafari system at infinity by using the Poincar´e compactification of a polynomial vector fi...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Published: |
World Scientific Publishing
2016
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| Summary: | To understand the complex dynamics of Kingni-Jafari system with hidden attractors, the first objective of this paper was to study the global dynamics, and give a complete description of the dynamics of Kingni-Jafari system at infinity by using the Poincar´e compactification of a polynomial vector field in R3. The second objective of this paper was to proof the existence of periodic solutions in the Kingni-Jafari system by classic Hopf bifurcation and degenerate Hopf bifurcation. Moreover, based on averaging theory, a small amplitude periodic solution that bifurcate from a zero-Hopf equilibrium was derived in the Kingni-Jafari system. The theoretical analysis and simulations demonstrate the rich dynamics of the system |
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