Coexistence of multiple attractors and crisis route to chaos in a novel chaotic jerk circuit. (English) Zbl 1343.34115
Summary: A novel autonomous RC chaotic jerk circuit is introduced and the corresponding dynamics is systematically investigated. The circuit consists of opamps, resistors, capacitors and a pair of semiconductor diodes connected in anti-parallel to synthesize the nonlinear component necessary for chaotic oscillations. The model is described by a continuous time three-dimensional autonomous system with hyperbolic sine nonlinearity, and may be viewed as a linear transformation of model MO15 previously introduced in [J. C. Sprott, Elegant chaos. Algebraically simple chaotic flows. Hackensack, NJ: World Scientific (2010; Zbl 1222.37005)]. The structure of the equilibrium points and the discrete symmetries of the model equations are discussed. The bifurcation analysis indicates that chaos arises via the usual paths of period-doubling and symmetry restoring crisis. One of the key contributions of this work is the finding of a region in the parameter space in which the proposed (“elegant”) jerk circuit exhibits the unusual and striking feature of multiple attractors (i.e. coexistence of four disconnected periodic and chaotic attractors). Laboratory experimental results are in good agreement with the theoretical predictions.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 94C05 | Analytic circuit theory |
| 34D45 | Attractors of solutions to ordinary differential equations |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
Keywords:
jerk system with hyperbolic sine nonlinearity; electronic circuit implementation; routes to chaos; coexistence of multiple attractors; experimental studyCitations:
Zbl 1222.37005References:
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