4 papers
Metastable periodic patterns in singularly perturbed state dependent delayed equations
Xavier Pellegrin, Clodoaldo Grotta Ragazzo, Coraci Malta +1
We consider the scalar delayed differential equation $\ep\dot x(t)=-x(t)+f(x(t-r))$, where $\ep>0$, $r=r(x,\ep)$ and represents either a positive feedback or a negati…
Coherence transition in degenerate diffusion equations with mean field coupling
Khashayar Pakdaman, Xavier Pellegrin
We introduce non-linear diffusion in a classical diffusion advection model with non local aggregative coupling on the circle, that exhibits a transition from an uncoherent state to…
Transitions in active rotator systems: invariant hyperbolic manifold approach
Giambattista Giacomin, Khashayar Pakdaman, Xavier Pellegrin +1
Our main focus is on a general class of active rotators with mean field interactions, that is globally coupled large families of dynamical systems on the unit circle with non-trivi…
Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators
Giambattista Giacomin, Khashayar Pakdaman, Xavier Pellegrin
We study the dynamics of the large N limit of the Kuramoto model of coupled phase oscillators, subject to white noise. We introduce the notion of shadow inertial manifold and we pr…