Bifurcations of Double Homoclinic Loops with Inclination Flip and Nonresonant Eigenvalues (Journal of Nonlinear Modeling and Analysis, 2024)
In this work, bifurcation analysis near double homoclinic loopswith $W^s$ inclination flip of $Γ_1$ and nonresonant eigenvalues is presented in afour-dimensional system. We establish a Poincaré map by constructing localactive coordinates approach in some tubular neighborhood of unperturbeddouble homoclinic loops. Through studying the bifurcation equations, weobtain the condition that the original double homoclinic loops are persistent,and get the existence or the nonexistence regions of the large 1-homoclinicorbit and the large 1-periodic orbit. At last, an analytical example is given toillustrate our main results.