Related papers: For how long time evolution of chaotic or random s…
The dynamics of an infinite continuum system of randomly jumping and coalescing point particles is studied. The states of the system are probability measures on the corresponding configuration space $\Gamma$ the evolution of which is…
Predicting extreme events in chaotic systems, characterized by rare but intensely fluctuating properties, is of great importance due to their impact on the performance and reliability of a wide range of systems. Some examples include…
Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have…
A new element is proposed to play a role in the evolution of extrasolar planetary systems: the tidal (or elliptical) instability. It comes from a parametric resonance and takes place in any rotating fluid whose streamlines are (even…
For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic…
Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the time to extinction is an important characteristic of any natural population. Here we consider logistic and logistic-like systems under the combined…
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…
This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
When a chaotic, ergodic Hamiltonian system with $N$ degrees of freedom is subject to sufficiently rapid periodic driving, its energy evolves diffusively. We derive a Fokker-Planck equation that governs the evolution of the system's…
We perform a detailed analysis of the behavior of coherent and squeezed states undergoing time evolution. We calculate time dependence of expectation values of position and momentum in coherent and squeezed states (which can be interpreted…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the…
In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration…
An experimental approach is taken to study the dynamics of the dripping water faucet, a simple deterministic system. The time interval between successive drops may be affected by the many drops preceding it. The time interval is predicted…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as…