(1) Department of Applied Mathematics and Informatics, Faculty of Science and Technology, Ryukoku University, Seta Ohtsu, 520-2194, Japan;(2) Department of Mathematical Science, Montana State University, Bozeman, Montana, 59717
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.