Further nonlinear dynamical analysis of simple jerk system with multiple attractors. (English) Zbl 1372.37096
Summary: This paper presents an analytical framework to investigate the dynamical behavior of a recent chaotic jerk model with multiple attractors. The methods of analytical analysis are adopted to complement numerical approach employed previously. In order to accomplish this goal, first, we amend the form of original system to a more general form and then apply both normal form theory and perturbation methods in order to investigate various dynamical behaviors exhibited by the system. The codimension one and codimension two bifurcations including pitchfork, Hopf, Bogdanov-Takens and generalized Hopf bifurcations are examined. The stability of bifurcated limit cycles is studied. The approximate solutions of homoclinic orbit and unstable limit cycle arising in the system are attained. The changes in dynamics relative to new parameters introduced in the model are also traced. Finally, numerical simulations and proposed circuit realization of the model are presented so as to validate theoretical results. We demonstrate that the jerk model has rich dynamics that make it ideal in realization of various applications including secure communications systems.
MSC:
| 37G10 | Bifurcations of singular points in dynamical systems |
| 34C37 | Homoclinic and heteroclinic solutions to ordinary differential equations |
| 37C29 | Homoclinic and heteroclinic orbits for dynamical systems |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 94A60 | Cryptography |
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