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Symmetry Breaking and Conserving Blow-out Bifurcations in Coupled Chaotic Systems

Symmetry Breaking and Conserving Blow-out Bifurcations in Coupled Chaotic Systems.  Symmetrically Coupled 1D Maps. Woochang Lim and Sang-Yoon Kim Department of Physics Kangwon National University. Invariant Synchronization Line:. Appearance of A Synchronous Chaotic

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Symmetry Breaking and Conserving Blow-out Bifurcations in Coupled Chaotic Systems

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  1. Symmetry Breaking and Conserving Blow-out Bifurcations in Coupled Chaotic Systems •  Symmetrically Coupled 1D Maps Woochang Lim and Sang-Yoon Kim Department of Physics Kangwon National University Invariant Synchronization Line: Appearance of A Synchronous Chaotic Attractor (SCA) on The Invariant Synchronization Line when Crossing Critical Lines in The a-c Plane

  2. Blow-out Bifurcations SCA with a negative transverse Lyapunov exponent Blow-out Bifurcation SCA Chaotic Saddle with Absorbing Area (Trapping and Superattracting Region)  Appearance of The Asynchronous Chaotic Attractor through A Supercritical Blow-out Bifurcation

  3. Minimal Invariant Absorbing Area • Parameter Mismatching:  Existence and shape of a minimal invariant absorbing area can be ascertained Minimal invariant absorbing area bounded by segments of the critical curves After a parameter mismatching

  4. Symmetry Conserving Blow-out Bifurcation • Symmetric Minimal Absorbing Area before The Blow-out Bifurcation • Appearance of Symmetric Chaotic Attractor through A Symmetry Conserving Blow-out Bifurcation for

  5. Symmetry Breaking Blow-out Bifurcation (a=1.427) • Asymmetric Minimal Absorbing Area before The Blow-out Bifurcation • Appearance of Asymmetric Chaotic Attractor through A Symmetry Breaking Blow-out Bifurcation for

  6. Symmetry Conserving Blow-out Bifurcation for The Dissipatively-coupled Case Before the blow-out bifurcation After the blow-out bifurcation

  7. Summary The Shape of The Minimal Invariant Absorbing Area Determines The Type of Blow-out Bifurcations Symmetric (Asymmetric) Absorbing Area before The Blow-out Bifurcation  Appearance of Symmetric (Asymmetric) CA through A Symmetry Conserving (Breaking) Blow-out Bifurcation Future Works on The Global Effects of The Blow-out Bifurcation Investigation of The Global Effects of The Symmetry-Conserving and -Breaking Blow-out Bifurcation in Terms of The Unstable Periodic Orbits.

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