Piecewise Linear Analogue of Hopf-Zero Bifurcation in an Extended BVP Oscillator

In this work, we consider a family of symmetric piecewise linear systems in three dimensions. By using the analysis done in Ponce et al. (Physica D 250: 34-46, 2013), in which the authors detect and characterize the appearance of limit cycles for the bifurcation parameter passing through its critical value, we show that Hopfzero bifurcation takes place for a certain range of parameters in an extended version of Bonhoeffer-van der Pol oscillator.