On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry

• Non-symmetric planar continuous piecewise-linear differential systems are studied.
• Some results about the existence and uniqueness of their limit cycles are given.
• For systems with three linear zones and no symmetries new results are obtained.
• For systems with two linear zones a shorter proof of known results is achieved.
• The application to the McKean model of a single neuron activity is described.

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems.New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter proofs of known results.A relevant application to the McKean piecewise linear model of a single neuron activity is included.