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Planar systems of piecewise linear differential equations with a line of discontinuity
Nonlinearity, 2001The authors study dynamical properties of the planar system \[ \dot u= Au+sgn( w^{T}u) v, \] where \(A\) is a real \(2\times 2\)-matrix and \(u, v, w\) are two-dimensional real vectors. The dependence on the system parameters \(A,v\) and \(w,\) including the existence of periodic solutions with sliding motion, is analyzed.
Giannakopoulos, Fotios, Pliete, Karin
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From Linear to Piecewise Linear Differential Systems
2022Enrique Ponce, Javier Ros, Elisabet Vela
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Pseudo-Cusp Bifurcation in a Class of 3D Piecewise Linear Differential Systems
International Journal of Bifurcation and ChaosConsider the nongeneric family of 3D piecewise linear differential systems, with a discontinuity plane that has two parallel invisible tangency lines, such that the region between them is the sliding region. It is known that the change of stability of the sliding region gives rise to a Crossing Limit Cycle (CLC).
Bruno Campoy +2 more
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Piecewise constant control of boundary value problem for linear impulsive differential systems
2007A piecewise constant control that solves the boundary value problem for linear impulsive differential systems is considered. We establish a necessary and sufficient conditions for the existence of such control. Moreover, a result that explicitly characterizes the solving control is presented.
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At most two limit cycles in a piecewise linear differential system with three zones and asymmetry
Physica D: Nonlinear Phenomena, 2019Hebai Chen, Yilei Tang
exaly
Piecewise linear differential systems with only centers can create limit cycles?
Nonlinear Dynamics, 2017Jaume Llibre, Marco Antonio Teixeira
exaly