Abstract
In this study we examine a symmetry-breaking bifurcation of homoclinic orbits in diffusively coupled ordinary differential equations. We prove that asymmetric homoclinic orbits can bifurcate from a symmetric homoclinic orbit when the equilibria to which the latter is homoclinic undergoes a pitchfork bifurcation. A condition which defines the direction of the bifurcation in a parameter space is given. All hypotheses of the main theorem are verified for a diffusively coupled logistic system and the twistedness of the bifurcating homoclinic orbits is computed for a range of coupling strengths.
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Morita, Y., Dockery, J. & Pernarowski, M. Symmetry-Breaking Homoclinic Bifurcations in Diffusively Coupled Equations. Journal of Dynamics and Differential Equations 13, 613–649 (2001). https://doi.org/10.1023/A:1016638408053
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DOI: https://doi.org/10.1023/A:1016638408053