5 papers
Limit cycles in piecewise smooth systems with circular switching manifold
Gabriel Rondón, Paulo R. da Silva, Jaume Llibre
We study limit cycles in piecewise complex systems with switching manifold . Using Möbius transformations we establish an equivalence between circular and straight-l…
Complex potentials and holomorphic differential equations
Gabriel Rondón, Paulo R. da Silva
A complex potential is a holomorphic function whose real and imaginary parts generate a pair of orthogonal foliations, representing the equipotential…
Global Centers and Phase Portraits in Generalized Duffing Oscillators: A Comprehensive Study of the Center-Focus Problem
Gabriel Rondón, Nasrin Sadri
This work presents a comprehensive study of the generalized Duffing oscillator, a fundamental model in nonlinear dynamics described by the system $$ \dot{x} = y, \quad \dot{y} = -Î…
The dynamics of the Ehrhard-Müller system with invariant algebraic surfaces
Jaume Llibre, Gabriel Rondón
In this paper we study the global dynamics of the Ehrhard-Müller differential system \[ \dot{x} = s(y - x), \quad \dot{y} = rx - xz - y + c, \quad \dot{z} = xy - z, \] where ,…
Simultaneous bifurcation of limit cycles for Piecewise Holomorphic systems
Armengol Gasull, Gabriel Rondón, Paulo R. da Silva
Let be a holomorphic differential equation with center at . In this paper we are concerned about studying the piecewise perturbation systems $\dot{z}=f(z)+εR^\pm…