Related papers: Self-organized escape of oscillator chains in nonl…
Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the…
The erratic nature of chaotic behavior is thought to erode the stability of periodic behavior, including topological oscillations. However, we discover that in the presence of chaos, non-trivial topology not only endures but also provides…
We consider a chain of $n$ coupled oscillators placed on a one-dimensional lattice with periodic boundary conditions. The interaction between particles is determined by a weakly anharmonic potential $V_n = r^2/2 + \sigma_nU(r)$, where $U$…
We consider white noise perturbations of a nonlinear dynamical system in the neighborhood of an unstable critical point with linearization given by a Jordan block of full dimension. For the associated exit problem, we study the joint…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
This paper focuses on the escape problem of a harmonically-forced classical particle from a purely-quartic truncated potential well. The latter corresponds to various engineering systems that involve purely cubic restoring force and absence…
We present a general geometrical approach to the problem of escape from a metastable state in the presence of noise. The accompanying analysis leads to a simple condition, based on the norm of the drift field, for determining whether…
We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
We consider two particles hopping on a chain with a contact interaction between them. At strong interaction, there is a molecular bound state separated by a direct gap from a continuous band of atomic states. Introducing weak disorder in…
We present a chemical reaction network that is unstable under deterministic mass action kinetics, exhibiting finite-time blow-up of trajectories in the interior of the state space, but whose stochastic counterpart is positive recurrent.…
This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain (a nonintegrable system) and compares the simulation results with the theoretical results in fluid (an integrable system). Three…
Synchronized oscillations are of critical functional importance in many biological systems. We show that such oscillations can arise without centralized coordination in a disordered system of electrically coupled excitable and passive…
In this work, we present a simple and efficient generator of polymeric linear chains, based on a random self-avoiding walk process. The chains are generated using a discrete process of growth, in cubic networks and in a finite time, without…
An important characteristic of flocks of birds, school of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added…
We demonstrate the mechanisms of emergence and the link between two types of symmetry-broken states, the unbalanced periodic two-cluster states and solitary states, in coupled excitable systems with prevalent repulsive interactions.…
Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point…
While the existence of polar ordered states in active systems is well established, the dynamics of the self-assembly processes are still elusive. We study a lattice gas model of self-propelled elongated particles interacting through…
Many-body and complex systems, both classical and quantum, often exhibit slow, nonlinear relaxation toward stationary states due to the presence of metastable configurations and environmental fluctuations. Nonlinear relaxation in a wide…
We discuss the process by which energy, initially evenly distributed in a nonlinear lattice, can localize itself into large amplitude excitations. We show that, the standard modulational instability mechanism, which can initiate the process…