Related papers: Finite-time scaling on low-dimensional map bifurca…

We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an…

We consider regular lattices of coupled chaotic maps. Depending on lattice size, there may exist a window in parameter space where complete synchronization is eventually attained after a transient regime. Close outside this window, an…

This paper proposes a new distributed finite-time differentiator (DFD) for multi-agent systems (MAS) under directed graph, which extends the differentiator algorithm from the centralized case to the distributed case by only using…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

For the 2D matrix Langevin dynamics that corresponds to the continuous-time limit of the product of some $2 \times 2$ random matrices, the finite-time Lyapunov exponent can be written as an additive functional of the associated Riccati…

Finite-size scaling expressions for the current near the continuous phase transition, and for the local density near the first-order transition, are found in the steady state of the one-dimensional fully asymmetric simple-exclusion process…

Critical points with emergent symmetry exhibit intriguing scaling properties induced by two divergent length scales, attracting extensive investigations recently. We study the driven critical dynamics in a three-dimensional $q$-state clock…

Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…

We investigate finite-size effects on the chiral phase diagram of strong interactions within the linear sigma model coupled to quarks. We estimate the modification of the pseudocritical transition line and isentropic trajectories for sizes…

We study a dynamical phase transition in optical bistable systems subject to a time-periodic driving field. The phase transition occurs in the structure of limit cycle as a function of the frequency of the driving field. In the…

Instabilities in 1D spatially extended systems are studied with the aid of both temporal and spatial Lyapunov exponents. A suitable representation of the spectra allows a compact description of all the possible disturbances in tangent…

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…

This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

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…

Using direct numerical simulation we study the behavior of the maximal Lyapunov exponent in thin-layer turbulence, where one dimension of the system is constrained geometrically. Such systems are known to exhibit transitions from fully…

Systems where time evolution follows a multiplicative process are ubiquitous in physics. We study a toy model for such systems where each time step is given by multiplication with an independent random $N\times N$ matrix with complex…

Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…

We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. It…

We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…