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math.DS2026
Limit Cycles in a Discontinuous Generalized Liénard Systems with Bivariate Perturbation
Carlos F. Álvarez, Alexander Sierra-Ortiz
We study the number of limit cycles of the piecewise smooth differential system \[ \dot{x}=y, \quad \dot{y}=-x-\varepsilon\bigl(f(x)y+\operatorname{sgn}(x)g(x,y)\bigr),\] where $f(…
math.DS2026
Topological Detection of Hopf Bifurcations via Persistent Homology: A Functional Criterion from Time Series
Jhonathan Barrios, Yásser Echávez, Carlos F. Álvarez
We propose a topological framework for detecting Hopf-type dynamical transitions directly from scalar time series. The method combines delay-coordinate reconstruction with persiste…