Related papers: Bogdanov-Takens resonance in time-delayed systems
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…
We calculate the period of recurrence of dynamical systems comprising two interacting bosons. A number of theoretical issues related to this problem are discussed, in particular, the conditions for small periodicity. The knowledge gathered…
We study the dynamics of perturbations in time delayed dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be mapped to the linear…
We have demonstrated that a rather weak external optical feedback with delay can lead to the mode switching of the counterpropogating modes. The delay time should be longer then any system characteristic time. The equations describing the…
It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted…
Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
This article provides an example of fast-slow system such that most orbits remain as close as possible to the unstable manifold of the fast dynamics for an arbitrarily long time.
This study investigates the dynamics of a magnetic pendulum under time-varying magnetic excitation with a position-dependent phase. The system exhibits complex chaotic and regular dynamics, validated through simulations and experiments. The…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
We investigate the dynamics of a soliton that behaves as an extended particle. The soliton motion in an effective bistable potential can be chaotic in a similar way as the Duffing oscillator. We generalize the concept of geometrical…
The dynamics of self-oscillatory extended systems, resonantly forced at a frequency close to that of the natural oscillations (1:1 resonance), is shown to be universally described by a complex Ginzburg-Landau equation containing an…
We analyze canard explosions in delayed differential equations with a one-dimensional slow manifold. This study is applied to explore the dynamics of the van der Pol slow-fast system with delayed self-coupling. In the absence of delays,…
We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven…
Strong frequency dependence is unlikely in diffusive or over-damped systems. When exceptions do occur, such as in the case of stochastic resonance, it signals an interesting underlying phenomenon. We find that such a case appears in the…
Effects of time-delayed-feedback on pattern formation are studied in symmetrical bistable media. The results show that the time delay alters the behavior of the front bifurcation remarkably. The critical point of the Nonequilibrium…
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…
We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification…