Related papers: Mode hopping strongly affects observability of dyn…
We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…
We present the qualitative differences in the phase transitions of the mono-mode Dicke model in its integrable and chaotic versions. We show that a first order phase transition occurs in the integrable case whereas a second order in the…
We analyze the nonlinear dynamics of a high-finesse optical cavity in which one mirror is mounted on a flexible mechanical element. We find that this system is governed by an array of dynamical attractors, which arise from phase-locking…
Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With…
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…
Normal--mode splitting is the most evident signature of strong coupling between two interacting subsystems. It occurs when two subsystems exchange energy between themselves faster than they dissipate it to the environment. Here we…
Biochemical reactions with oscillatory behavior play an essential role in synthetic biology at the microscopic scale. Although a robust stability theory for deterministic chemical oscillators in the macroscopic limit exists, the dynamical…
We study dendritic growth numerically with a phase field model. Tip oscillation and regular side-branching are observed in a parameter region where the anisotropies of the surface tension and the kinetic effect compete. The transition from…
We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect…
We explore the impact of weak disorder on the dynamics of classical particles in a periodically oscillating lattice. It is demonstrated that the disorder induces a hopping process from diffusive to regular motion i.e. we observe the…
This paper shows that the variance of load bus voltage magnitude in a small power system test case increases monotonically as the system approaches a Hopf bifurcation. This property can potentially be used as a method for monitoring…
Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
Driven by a sufficiently powerful pump laser, a cavity optomechanical system will stabilize in coupled oscillations of its cavity field and mechanical resonator. It was assumed that the oscillation will be continuously magnified upon…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
The exotic phase transitions and multistabilities in atom-cavity coupled systems have attracted tremendous interests recently. In this work, we investigate the effect of photon hopping between two Dicke cavities, which induces rich quantum…
This work addresses non-classically damped coupled oscillators with closely spaced modes focusing on the physics of modal interactions. Considering the simplest representative example in the form of an impulsively excited…
Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where…
We study self-oscillations of an optomechanical system, where coherent mechanical oscillations are induced by a driven optical or microwave cavity, for the case of an anharmonic mechanical oscillator potential. A semiclassical analytical…