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arXiv · 2608.10581

Hopf-like bifurcations induced by hysteresis and time-delay near monodromic tangential singularities

Douglas D. Novaes·Paulo Santana·David J. W. Simpson
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Abstract

We investigate planar piecewise-analytic vector fields, focusing on the merged focus and other monodromic tangential singularities when hysteresis or time-delay is incorporated into the switching condition. If the singularity is an asymptotically stable solution of the system with an instantaneous switch, then the introduction of hysteresis or time-delay causes an attracting limit cycle to be formed locally. We derive asymptotic expressions for the size and period of the limit cycle, allowing any degrees of tangency and any order for the smallest non-zero Lyapunov coefficient. We find that the growth rate of the limit cycle differs for hysteresis and time-delay, and differs to that of the related pseudo-Hopf bifurcation.

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Douglas D. Novaes, Paulo Santana, David J. W. Simpson. 2026-08-11. Hopf-like bifurcations induced by hysteresis and time-delay near monodromic tangential singularities. https://arxiv.org/abs/2608.10581

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