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Stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation…
We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…
Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as…
Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
Previous study of properties of the first-order phase transition in a set of plasma mod-els with common feature - absence of individual correlations between charges of opposite sign, was continued. Predicted discontinuities in equilibrium…
Bursting is a phenomenon found in a variety of physical and biological systems. For example, in neuroscience, bursting is believed to play a key role in the way information is transferred in the nervous system. In this work, we propose a…
This paper presents a new systematic framework for nonlinear singularly perturbed systems in which state-dependent perturbation functions are used instead of constant perturbation coefficients. Under this framework, general results are…
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…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend…
We study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
General scenarios of transitions between different spot patterns on electrodes of dc gas discharges and their relation to bifurcations of steady-state solutions are analyzed. In the case of cathodes of arc discharges, it is shown that any…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
We consider the one-dimensional Swift-Hohenberg equation coupled to a conservation law. As a parameter increases the system undergoes a Turing bifurcation. We study the dynamics near this bifurcation. First, we show that stationary,…
We investigate the steady-state phases of the one-dimensional quantum contact process model. We present the Liouvillian gap in the thermodynamic limit and uncover the metastability of the system. Exploiting the mean-field approximations…
Autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as extinction of…
The stability of high vs. low spin states of transition metal complexes has been interpreted by ligand field theory, which is a perturbation theory of the electron-electron interaction. The present first principles calculation of a series…
We study formally and rigorously the bifurcation to steady and time-periodic states in a model for a thin superconducting wire in the presence of an imposed current. Exploiting the PT-symmetry of the equations at both the linearized and…