3 papers
math.DS2025★ 1 cited
Classification of global attractors for -equivariant parabolic equations: a survey
Carlos Rocha, Bernold Fiedler, Alejandro López-Nieto
We survey the global dynamics of semiflows generated by scalar semilinear parabolic equations which are equivariant under spatial shifts of $x\in \mathbb{S}^1=\mat…
math.DS2025
Periodicity in delayed self-regulation is a predator-prey process
Alejandro López-Nieto
We unify two different periodicity mechanisms: delayed self-regulation and planar predator-prey feedback. We consider scalar delay differential equations $\dot x(t) = rf(x(t), x(t…
math.DS2023
Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria
Alejandro López-Nieto, Phillipo Lappicy, Nicola Vassena +2
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a…