Related papers: Temporal oscillations in Becker-Doering equations …
I consider the problem of self-oscillatory systems undergoing a homogeneous Hopf bifurcation when they are submitted to an external forcing that is periodic in time, at a frequency close to the system's natural frequency (1:1 resonance),…
We discuss an approach to the computer assisted proof of the existence of branches of stationary and periodic solutions for dissipative PDEs, using the Brussellator system with diffusion and Dirichlet boundary conditions as an example, We…
For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have…
We study the emergence and the stability of temporal localized structures in the output of a semiconductor laser passively mode-locked by a saturable absorber in the long cavity regime. For large yet realistic values of the linewidth…
A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $\epsilon$. The random fluctuations of the system at the critical point are studied…
In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and…
A coupled-phase oscillator model where each oscillator has an angular velocity that varies due to the interaction with other oscillators is studied. This model is proposed to deepen the understanding of the relationship between the…
We examine the dynamics of solutions to nonlinear Schrodinger/Gross-Pitaevskii equations that arise due to Hamiltonian Hopf (HH) bifurcations--the collision of pairs of eigenvalues on the imaginary axis. To this end, we use inverse…
The spatiotemporal patterns of a reaction diffusion mussel-algae system with a delay subject to Neumann boundary conditions is considered. The paper is a continuation of our previous studies on delay-diffusion mussel-algae model. The global…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
In this paper we analyze a generic dynamical system with $\mathbb{D}_2$ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from…
We study networks of theta neurons arranged on a ring with delayed interactions. In the continuum limit the systems are described by next generation neural field models with delays. We consider distributed delays with both finite and…
We describe the asymptotic behaviour of solutions of unviscid Burgers equation on the circle with time-periodic forcing. These solutions converge to periodic states, but the period of these limit states may be greater than the period of the…
Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we…
In this work we propose a feedback approach to regulate the chaotic behavior of the whole family of the generalized Lorenz system, by designing a nonlinear delayed feedback control. We first study the effect of the delay on the dynamics of…
We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate Hopf bifurcations in ordinary and delay differential equations. We apply the method to rigorously investigate these nonlocal bifurcation…
Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic…
We study collective dynamics of networks of mutually coupled identical Lorenz oscillators near subcritical Hopf bifurcation. This system shows induced multistable behavior with interesting spatio-temporal dynamics including synchronization,…
We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our…