Center bifurcation for Two-Dimensional Border-Collision Normal Form

In this work we study some properties associated with the bordercollision bifurcations in a two-dimensional piecewise linear map in canonical form, related to the case in which a ...xed point of one of the linear maps has complex eigenvalues and undergoes a center bifurcation when its eigenvalues pass through the unit circle. This problem is faced in several applied piecewise smooth models, such as switching electrical circuits, impacting mechanical systems, business cycle models in economics, etc. We prove the existence of an invariant region in the phase space for parameter values related to the center bifurcation and explain the origin of a closed invariant attracting curve after the bifurcation. This problem is related also to particular border-collision bifurcations leading to such curves which may coexist with other attractors. We show how periodicity regions in the parameter space di

• Type: Journal
• Year: 2008
• Where: IJBC
• Authors: Iryna Sushko, Laura Gardini
• Keywords: Center Bifurcation, IJBC 2008, Neimark-Sacker Bifurcation, Smooth Models