New analytical technique for predicting homoclinic bifurcations in autonomous dynamical systems
The author considers planar differential equations \(\dot{x} = y\), \(\dot{y} = -\lambda x + \epsilon f(x,y,\mu)\), where \(\epsilon\) is a small parameter and \(\mu\) are other parameters. Approximating solutions by averaging, equations for homoclinic solutions are derived by looking for collisions of limit cycles with equilibria of saddle type. Not much justification is given, but a number of examples are discussed where the results are compared with Melnikov's method to locate homoclinic solutions.
scientific article; zbMATH DE number 1216529