Related papers: Discrete Dynamical Systems with Random Impulses
We study the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class.…
We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
In this paper, we develop a novel contraction framework for stability analysis of discrete-time nonlinear systems with parameters following stochastic processes. For general stochastic processes, we first provide a sufficient condition for…
Properties of the noise-driven escape kinetics are mainly determined by the stochastic component of the system dynamics. Nevertheless, the escape dynamics is also sensitive to deterministic forces. Here, we are exploring properties of the…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
Spontaneous directed motion, a hallmark of cell biology, is unusual in classical statistical physics. Here we study, using both numerical and analytical methods, organized motion in models of the cytoskeleton in which constituents are…
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…
We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently…
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in…
In this work, we begin the study of a new class of dynamical systems determined by interval maps generated by the symbolic action of erasing substitution rules. We do this by discussing in some detail the geometric, analytical, dynamical…
We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…