Related papers: Self Organization of Interacting Polya Urns
Self-organized criticality (SOC) reveals a mechanism by which a system is autonomously evolved to be in a critical state without needing parameter tuning. Whereas various biological systems are found to be in critical states and the…
We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…
The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is…
We study a normalized two dimensional competitive Lotka$-$Volterra system describing the interaction between state power and society power. Restricting attention to the positively invariant domain $[0,1]^2$, the analysis focuses on interior…
One new thing often leads to another. Such correlated novelties are a familiar part of daily life. They are also thought to be fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities,…
Dynamical urn models, such as the Ehrenfest model, have played an important role in the early days of statistical mechanics. Dynamical many-urn models generalize the former models in two respects: the number of urns is macroscopic, and…
In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organized criticality, a specific type of non-equilibrium…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free…
Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field theoretic renormalization group. The stirring and mixing are modelled by a random…
We introduce a simple ecological model describing the spatial organization of two interacting populations whose individuals are indifferent to conspecifics and avoid the proximity to heterospecifics. At small population densities $\Phi$ a…
Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
Self-organization phenomena in ensembles of self-propelled particles open pathways to the synthesis of new dynamic states not accessible by traditional equilibrium processes. The challenge is to develop a set of principles that facilitate…
Prions are misfolded proteins that transmit their structural arrangement to neighboring proteins. In biological systems, prion dynamics can produce a variety of complex functional outcomes. Yet, an understanding of prionic causes has been…
We consider a mean-field dynamical urn model, defined by rules which give the rate at which a ball is drawn from an urn and put in another one, chosen amongst an assembly. At equilibrium, this model possesses a fluid and a condensed phase,…
Sand pile formation is often used to describe stratified chaos in dynamic systems due to self-emergent and scale invariant behaviour. Cellular automata (Bak-Tang-Wiesenfeld model) are often used to describe chaotic behaviour, as simulating…
Cold pools (CPs) contribute to convective organization. However, it is unclear by which mechanisms organization occurs. By using a particle method to track CP gust fronts in large eddy simulations, we characterize the basic collision modes…
Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…
Dynamic Complexity is a phenomenon exhibited by a nonlinearly interacting system within which multitudes of different sizes of large scale coherent structures emerge, resulting in a globally nonlinear stochastic behavior vastly different…