Related papers: Self-Organized Criticality and Punctuated Equilibr…
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
We investigate the temporal dynamics of the Ikeda Map with Balanced Gain and Loss and in the presence of feedback loops with saturation nonlinearity. From the bifurcation analysis, we find that the temporal evolution of optical power…
We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a…
We review the close link between intermittent events ('quakes') and extremal noise fluctuations which has been advocated in recent numerical and theoretical work. From the idea that record-breaking noise fluctuations trigger the quakes, an…
We study small random perturbations by additive white-noise of a spatial discretization of a reaction-diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with…
A minimal model based on individual interactions is proposed to study the non-Poisson statistical properties of human behavior: individuals in the system interact with their neighbors, the probability of an individual acting correlates to…
We show that the coupled complex systems can evolve into a new kind of self-organized critical state where each subsystem is not critical, however, they cooperate to be critical. This criticality is different from the classical BTW…
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For…
Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
The steady state shock formation in processes like nonconserving asymmetric simple exclusion processes in varied situations is shown to be a nonequilibrium critical phenomenon. The diverging length scales and the quantitative description of…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
Multistability is an inseparable feature of many physical, chemical and biological systems which are driven far from equilibrium. In these nonequilibrium systems, stochastic dynamics often induces switching between distinct states on…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
Spontaneous symmetry-breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation, but the equilibrium states observed in nature are not. Here, we prove that when a discrete symmetry is…
When can complex ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where species abundances keep fluctuating without going to extinction? We show that high-diversity spatially-extended systems, in…
Many natural, technological and social systems are inherently not in equilibrium. We show, by detailed analysis of exemplar models, the emergence of equilibrium-like behavior in localized or nonlocalized domains within non-equilibrium…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…