For citation:
de Feo O. ., Hasler M. . Approximate synchronization of chaotic attractors. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 4, pp. 73-80. DOI: 10.18500/0869-6632-2005-13-4-73-80
Approximate synchronization of chaotic attractors
This work presents a dynamical phenomenon strongly related with the problems of synchronization and control of chaotic dynamical systems. Considering externally driven homoclinic chaotic systems, it is shown experimentally and theoretically that they tend to synchronize with signals strongly correlated with the saddle cycles of their skeleton; furthermore, when they are perturbed with a generic signal, uncorrelated with their skeleton, their chaotic behavior is reinforced. This peculiar behavior of approximate synchronization has also been called qualitative resonance, underlining the fact that such chaotic systems tend to resonate/synchronize with those signals which are qualitatively similar to an observable of their skeleton.
- Afraimovich VS, Verichev NN, Rabinovich MI. Stochastic synchronization of oscillation in dissipative systems. Radiophys. Quantum Electron. 1986;29(9):795–803. DOI: 10.1007/BF01034476.
- De Feo O. Qualitative resonance of Shil’nikov-like strange attractors, part I: Experimental evidence. International Journal of Bifurcation and Chaos. 2004;14(3):873–891. DOI: 10.1142/S0218127404009570.
- De Feo O. Qualitative resonance of Shil’nikov-like strange attractors, part II: Mathematical analysis. International Journal of Bifurcation and Chaos. 2004;14(3):893–912. DOI: 10.1142/S0218127404009739.
- De Feo O, Maggio GM, Kennedy MP. The Colpitts oscillator: Families of periodic solutions and their bifurcations. International Journal of Bifurcation and Chaos. 2000;10(5):935–958. DOI: 10.1142/S0218127400000670.
- Doedel EJ, Keller HB, Kernevez JP. Numerical analysis and control of bifurcation problems, part I: Bifurcation in finite dimensions. International Journal of Bifurcation and Chaos. 1991;1(3):493–520. DOI: 10.1142/S0218127491000397.
- Doedel EJ, Champneys AR, Fairgrieve TF, Kuznetsov YA, Sandstede B, Wang XJ. AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with Hom Cont). Montreal, Canada, Motreal, Quebec, Canada: Computer Science Department, Concordia University; 1998.
- Bittanti S, Bittanti S, Colaneri P. Periodic Control. New York, NY: John Wiley & Sons; 1999. P. 59–74.
- Callier FM, Desoer CA. Linear System Theory. New York, NY: Springer-Verlag; 1991. 509 p. DOI: 10.1007/978-1-4612-0957-7.
- De Feo O. Self-emergence of chaos in identifying irregular periodic behavior. Chaos. 2003;13(4):1205–1215. DOI: 10.1063/1.1606631.
- De Feo O. Tuning chaos synchronization and anti-synchronization for applications in temporal pattern recognition. International Journal of Bifurcation and Chaos. 2005;15(12):3905–3921. DOI: 10.1142/S0218127405014386.
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