Related papers: Time periodicity and dynamical stability in two-bo…
We study the dynamical stability of the macroscopic quantum oscillations characterizing a system of three coupled Bose-Einstein condensates arranged into an open-chain geometry. The boson interaction, the hopping amplitude and the…
A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…
Recurrence time is evaluated for some initial quantum states in the one-dimensional Bose gas with repulsive short-range interactions. In the relatively strong and weak coupling cases some different types of initial states show almost…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
Compact planetary systems with more than two planets can undergo orbital crossings from planet-planet perturbations. The time which the system remains stable without orbital crossings has an exponential dependence on the initial orbital…
The lowest adiabatic potential expressed in hyperspherical coordinates is estimated for two boson systems in an external harmonic trap. Corresponding conditions for stability are investigated and the related structures are extracted for…
The effective potential is computed for two boson systems in one trap as a function of their two individual hyperadii and the distance between their centers. Zero-range interactions are used and only relative s-states are included.…
The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability…
Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
In this paper we consider a population consisting of two species, dynamics of which is defined by a quadratic stochastic operator with variable coefficients, making it discontinuous operator at two points. This operator depends on three…
We consider the problem of optimizing the steady state of a dynamical system in closed loop. Conventionally, the design of feedback optimization control laws assumes that the system is stationary. However, in reality, the dynamics of the…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
For some one-dimensional discrete-time autonomous population models, local stability implies global stability of the positive equilibrismo point. One of the known techniques is the enveloping method. In this paper we extend the enveloping…
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…