Related papers: Retracting fronts induce spatio-temporal intermitt…
A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
The properties of the fluctuations large enough to induce bifurcations at open chemical systems at steady constraints are studied. The fluctuations that come from the diffusion-induced noise are considered. It is a generic for the surface…
In this article we study the retrospective inverse problem. The retrospective inverse problem consists of in the reconstruction of a priori unknown initial condition of the dynamic system from its known final condition. Existence and…
The periodic motion of a classical point particle in a one-dimensional double-well potential acquires a surprising degree of complexity if friction is added. Finite uncertainty in the initial state can make it impossible to predict in which…
We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto…
The bifurcation transition is studied for the onset of intermittency analogous to the Pomeau-Manneville mechanism of type-I, but generalized for the presence of a quasiperiodic external force. The analysis is concentrated on the…
The spatial and temporal persistence, or first-return distributions are measured for slow combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
In this work we identify and investigate a novel bifurcation in conserved systems. This secondary bifurcation stops active phase separation in its nonlinear regime. It is then either replaced by an extended, system-filling, spatially…
We study a spatial diffusion process generated by velocity fluctuations of intermittent nature. We note that intermittence reduces the entropy production rate while enhancing the diffusion strength. We study a case of space-dependent…
It is well-known for vibro-impact systems that the existence of a periodic solution with a low-velocity impact (so-called grazing) may yield complex behavior of the solutions. In this paper we show that unstable periodic motions which pass…
We investigate the existence of stationary fronts in a coupled system of two sine-Gordon equations with a smooth, "hat-like" spatial inhomogeneity. The spatial inhomogeneity corresponds to a spatially dependent scaling of the sine-Gordon…
We propose a model to study the spatiotemporal dynamics of biocrust and vegetation cover on sand dunes. The model consists of two coupled partial nonlinear differential equations and includes diffusion and advection terms for modeling the…
The study and characterization of the diversity of spatiotemporal patterns generated when a rectangular layer of fluid is locally heated beneath its free surface is presented. We focus on the instability of a stationary cellular pattern of…