Rigorous verification of Poincare map generated by a continuous Piece-Wise linear vector field and its application
This paper provides algorithms in order to solve an interval implicit function of the Poincare map generated by a continuous piecewise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MAT LAB and INT LAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective.
poincare map continuous piece-wise linear vector field interval arithmetic canard computer assisted rigorous proof slow-fast system