Hopf bifurcation analysis of a new commensurate fractional-order hyperchaotic system. (English) Zbl 1314.34081
Summary: In this paper, a new fractional-order hyperchaotic system based on the Lorenz system is presented. The chaotic behaviors are validated by the positive Lyapunov exponents. Furthermore, the fractional Hopf bifurcation is investigated. It is found that the system admits Hopf bifurcations with varying fractional order and parameters, respectively. Under different bifurcation parameters, some conditions ensuring the Hopf bifurcations are proposed. Numerical simulations are given to illustrate and verify the results.
MSC:
| 34C23 | Bifurcation theory for ordinary differential equations |
| 37G10 | Bifurcations of singular points in dynamical systems |
| 34A08 | Fractional ordinary differential equations |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
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