Related papers: In--out intermittency in PDE and ODE models
We study spatiotemporal intermittency in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes where the STI lies in the directed percolation class, as well as regimes which show pure spatial…
The resistivity maximum at a temperature $T=T_{\mathrm{max}}$ is a recurring feature of bandwidth-tuned Mott systems, yet its meaning remains controversial: is it a coherence-incoherence crossover of an electronically homogeneous metal, or…
This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a…
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…
The covariant scale-invariant dynamics (SID) theory has recently been proposed as a possible explanation for the observed dynamical discrepancies in galaxies (Maeder & Gueorguiev 2020). SID implies that these discrepancies $-$ commonly…
The inverse cascade of magnetic energy occurs when helicity or rotational instability exists in the magnetohydrodynamic (MHD) system. This well known phenomenon has been considered as a basis for the large scale magnetic field in universe.…
For a system of ODEs defined on an open, convex domain $U$ containing a positively invariant set $\Gamma$, we prove that under appropriate hypotheses, $\Gamma$ is the graph of a $C^r$ function and thus a $C^r$ manifold. Because the…
We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the…
In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation.…
The sine-Gordon model in the presence of dynamical integrable defects is investigated. This is an application of the algebraic formulation introduced for integrable defects in earlier works. The quantities in involution as well as the…
We consider a non-autonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we…
Intermittency is one of central obstacles for understanding small-scale dynamics in the fully developed hydrodynamic turbulence. The modern approach is largely based on the multifractal theory of Parisi and Frisch which is, however,…
Context: Large-scale magnetic fields resulting from hydromagnetic dynamo action may differ substantially in their time dependence. Cyclic field variations, characteristic for the solar magnetic field, are often explained by an important…
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable…
The Rayleigh-Taylor (RT) instability is ubiquitously observed, yet has traditionally been studied using ideal fluid models. Collisionality can vary strongly across the fluid interface, and previous work demonstrates the necessity of kinetic…
In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time and ensemble average mean squared displacement are remarkably different. The ensemble average diffusivity is…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
Some ODE models treat ecological disturbance as a continuous process, even disturbances such as fire that occur almost instantaneously on the timescale of system recovery. Alternatively, flow-kick models resolve disturbances as discrete…
In his seminal work on turbulence, Kolmogorov made use of the stationary hypothesis to determine the Power Density Spectrum of the velocity field in turbulent flows. However to our knowledge, the constraints that stationary processes impose…
We consider the continuous-time setting of linear time-invariant (LTI) systems in feedback with multiplicative stochastic uncertainties. The objective of the paper is to characterize the conditions of Mean-Square Stability (MSS) using a…