Generalized synchronization of chaos via linear transformations. (English) Zbl 0937.37019

Summary: Generalized synchronization (GS) of two chaotic systems is a generalization of identical synchronization. Usually, the manifold of GS is much more complex than the driven system and the driving system. In this paper, the authors study a special case of GS in which the synchronization manifold is linear (linear GS for short). In a theorem, they present the necessary and sufficient conditions under which a linear GS can be achieved between two chaotic systems. In particular, they study the linear GS of two Chua’s circuits.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
Full Text: DOI


[1] DOI: 10.1109/31.75404 · doi:10.1109/31.75404
[2] DOI: 10.1142/S0218126694000090 · doi:10.1142/S0218126694000090
[3] DOI: 10.1109/81.538995 · doi:10.1109/81.538995
[4] DOI: 10.1103/PhysRevE.55.4029 · doi:10.1103/PhysRevE.55.4029
[5] DOI: 10.1515/FREQ.1992.46.3-4.66 · doi:10.1515/FREQ.1992.46.3-4.66
[6] DOI: 10.1142/S0218127496000187 · Zbl 0875.93182 · doi:10.1142/S0218127496000187
[7] DOI: 10.1109/81.536758 · doi:10.1109/81.536758
[8] DOI: 10.1142/S0218127496001727 · Zbl 1298.94112 · doi:10.1142/S0218127496001727
[9] DOI: 10.1109/81.572346 · Zbl 0884.94021 · doi:10.1109/81.572346
[10] DOI: 10.1142/S0218127497000443 · Zbl 0925.93374 · doi:10.1142/S0218127497000443
[11] DOI: 10.1109/81.633887 · doi:10.1109/81.633887
[12] DOI: 10.1142/S0218127498001200 · Zbl 0946.34047 · doi:10.1142/S0218127498001200
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