Related papers: Multibranch entrainment and slow evolution among b…

We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…

Superfluid and dissipative regimes in the dynamics of a two-component quasi-one-dimensional Bose-Einstein condensate (BEC) with unequal atom numbers in the components have been explored. The system supports localized waves of the symbiotic…

We study a generalized isotropic XY-model which includes both two-spin and four-spin mean-field interactions. This model can be solved in the microcanonical ensemble. It is shown that in certain parameter regions the model exhibits gaps in…

We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…

Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…

Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…

We consider several multiscale-in-time kinetic Monte Carlo models, in which some variables evolve on a fast time scale, while the others evolve on a slow time scale. In the first two models we consider, a particle evolves in a…

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We…

We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions with those in the non-interacting case…

We show that, for a one - dimensional open quantum system of ultracold atoms trapped in an array of harmonic potentials that is weakly coupled to a background Bose - Einstein Condensate (BEC), a unique steady state emerges at either of the…

We study one-dimensional spinless fermions with random interactions, but without any on-site disorder. We find that random interactions generically stabilize a many-body localized phase, in spite of the completely extended single-particle…

We study higher-order modulation instability phenomena in the frame of Manakov equations. Evolution that starts with a single pair of sidebands expands over several higher harmonics. The choice of initial pair of sidebands influences the…

Following our previous work in noncommutative braneworld inflation (arXiv:0911.4418), in this paper we use the smeared, coherent state picture of noncommutativity to study evolution of perturbations in a noncommutative braneworld scenario.…

We study a Bose-Einstein condensate (BEC) at low energy limit and show that their collective dynamics exhibit interesting topological behavior. The system undergoes dynamical topological phase transition at its global periods if its…

In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These `open Markov processes' serve as the building blocks for…

We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…

The misanthrope process is a class of stochastic interacting particle systems, generalizing the simple exclusion process. It allows each site of the lattice to accommodate more than one particle. We consider a special case of the one…

A system of neutral atoms trapped in an optical lattice and dispersively coupled to the field of an optical cavity can realize a variation of the Bose-Hubbard model with infinite-range interactions. This model exhibits a first order quantum…

We propose a new type of traveling wave pattern, one that can adapt to the size of physical system in which it is embedded. Such a system arises when the initial state has an instability that extends down to zero wavevector, connecting at…

Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world…