Related papers: A Two-Dimensional Map of Arbitrary Period
We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet…
This paper considers a nonlinear spherical pendulum whose suspension point performs high-frequency spatial vibrations. The dynamics of this pendulum can be described by averaging its Hamiltonian over phases of vibrations. Rotationally…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters…
We consider a single non-holonomic Dubins-like robot traveling with a constant longitudinal speed in an a priori unknown and unsteady planar environment. The robot should detect, locate, and track the boundary of a dynamic environmental…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
We consider a dynamical system to have memory if it remembers the current state as well as the state before that. The dynamics is defined as follows: $x_{n+1}=T_{\alpha}(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha)\cdot x_{n-1}),$…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solution pairs, it often enters prolonged slow-convergence…
In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism,…
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only…
Two bounds on the minimal time of dynamic rotating an initial state by arbitrary angle have been obtained. These bounds have been applied to study the evolutions in the Hadamard-Walsch gate, the Control-NOT quantum gate, and the Grover…
We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…
The motion of a simple pendulum in a uniform gravitational field can be described by the solution of a second-order differential equation, nonlinear differential equation. In practice we solve this equation using the small angle…
We study a family of dynamical systems obtained by coupling an Anosov map on the two-dimensional torus -- the chaotic system -- with the identity map on the one-dimensional torus -- the neutral system -- through a dissipative interaction.…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…