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 Chaotic Saddle with Blow-out Bifurcation Absorbing Area (Trapping and Superattracting Region)  Appearance of The Asynchronous Chaotic Attractor through A Supercritical Blow-out Bifurcation SCA

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