Related papers: Local Causal States and Discrete Coherent Structur…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
This contribution shortly outlines and reviews a theoretical and computational approach for a theory of change concerning systems where it is not possible to apply the laws of motion ab initio. The concept of meta-structure relates to the…
We investigate the emergence of localized coherent behavior in a system consisting of two populations of social agents possessing a condition for non-interacting states, mutually coupled through global interaction fields. As an example of…
From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress-generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry…
Spontaneous self-organization is ubiquitous in systems far from thermodynamic equilibrium. While organized structures that emerge dominate transport properties, universal representations that identify and describe these key objects remain…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
Chimera states have attracted significant attention as symmetry-broken states exhibiting the unexpected coexistence of coherence and incoherence. Despite the valuable insights gained from analyzing specific systems, an understanding of the…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
Macroscopic systems are described most completely by local densities (particle number, momentum and energy) yet the superposition states of such physical variables, indicated by the Everett interpretation, are not observed. In order to…
We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…
Mixing, and coherence are fundamental issues at the heart of understanding transport in fluid dynamics and other non-autonomous dynamical systems. Recently, the notion of coherence has come to a more rigorous footing, and particularly…
Quantum dynamics of coherent states is studied within quantum field theory using two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the…
Collective temporal organization in complex systems is commonly attributed to synchronization, resonance, or proximity to dynamical instabilities. Here we identify a distinct mechanism by which coherent, synchronization-like behavior can…
We report the occurrence of a self-emerging frequency chimera state in spatially extended systems of coupled oscillators, where the coherence and incoherence are defined with respect to the emergent frequency of the oscillations. This is…
The defining property of chimera states is the coexistence of coherent and incoherent domains in systems that are structurally and spatially homogeneous. The recent realization that such states might be common in oscillator networks raises…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…