Effect of Parameter Mismatch and Noise on The Loss of

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Presentation transcript:

Effect of Parameter Mismatch and Noise on The Loss of Chaos Synchronization W. Lim and S.-Y. Kim Department of Physics Kangwon National University  Unidirectionally-coupled 1D maps : Mismatching parameter : Noise strength : A uniform random variable with and a unit variance Invariant synchronization line: y = x A strongly stable synchronous chaotic attractor (SCA)

(Transcritical contact bifurcation) Riddling and Bubbling Transitions Weakly stable SCA Strongly stable SCA Weakly stable SCA c cr Riddling Transition (Transcritical contact bifurcation) cb Bubbling Transition (Supercritical PDB) Riddling transition when c decreases through cr (= -2.789 …) Basin of the SCA becomes riddled with a dense set of “holes” leading to the divergent orbits. Bubbling transition when c increases through cb (= -0.850 …) A typical trajectory starting near the diagonal first exhibits a transient intermittent bursting. But, it is eventually attracted to the SCA.

Chaotic Transients for The Riddling Case Parameter mismatch SCA with the riddled basin Chaotic transient

(long lived chaotic transient) Characterization of The Chaotic Transients : Average life-time of the chaotic transient c ~ -2.84 cr c Algebraic scaling Exponential scaling (long lived chaotic transient) Crossover

Effect of Noise for The Riddling Case Chaotic transient Effect of noise is the same as that of parameter mismatch. SCA with the riddled basin Noise Chaotic transient  Characterization of the chaotic transient

Effect of Parameter Mismatch and Noise for The Bubbling Case Parameter mismatch or noise  The SCA is broken up, and then it exhibits a persistent intermittent bursting.  Attractor bubbling The maximum bursting amplitude increases when passing c=cb. |y-x|max |y-x|max

Abrupt Change of The Maximum Bursting Amplitude The maximum bursting amplitude increases abruptly through the interior crisis of the absorbing area for c ~ -0.8437 Small absorbing area before the crisis Large absorbing area after the crisis Abrupt increase of the maximum bursting amplitude is in contrast to the case of symmetric coupling. Unidirectional coupling Symmetric coupling |y-x|max |y-x|max

Summary Effect of parameter mismatch and noise  Riddling case: Chaotic transient Average life-time of the chaotic transient  Crossover Exponential scaling Algebraic scaling (long lived chaotic transient)  Bubbling case: Attractor bubbling (Persistent intermittent bursting) Abrupt increase of the maximum bursting amplitude through the interior crisis of an absorbing area