Related papers: Self-organised-criticality and punctuated equilibr…
The notions of self-organised criticality (SOC) and turbulence are traditionally considered to be applicable to disjoint classes of phenomena. Nevertheless, scale-free burst statistics is a feature shared by turbulent as well as…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are…
A dynamic scaling Ansatz for the approach to the Self-Organized Critical (SOC) regime is proposed and tested by means of extensive simulations applied to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering the…
We describe blow-up behavior for ODEs by means of dynamics at infinity with complex asymptotic behavior in autonomous systems, as well as in nonautonomous systems. Based on preceding studies, a variant of closed embeddings of phase spaces…
We present a systematic study of dynamical heterogeneity in a model for permanent gels, upon approaching the gelation threshold. We find that the fluctuations of the self intermediate scattering function are increasing functions of time,…
Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of terms which correspond to individual 'processes' or 'fluxes'. Frequently, these…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
A self-organizing joint system classical oscillator + random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential equation. Various types of randomness…
One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on…
Paper is published in J. Phys. A: Math. Theor. 43 (2010) 225001, doi:10.1088/1751-8113/43/22/225001. Exact analytical solution for the universal probability distribution of the order parameter fluctuations as well as for the universal…
We introduce and study numerically a directed two-dimensional sandpile automaton with probabilistic toppling (probability parameter p) which provides a good laboratory to study both self-organized criticality and the far-from-equilibrium…
A methodology is developed to identify, as units of study, each decrease in the value of a stock from a given maximum price level. A critical level in the amount of price declines is found to separate a segment operating under a random walk…
Convection structures in binary fluid mixtures are investigated for positive Soret coupling in the driving regime where solutal and thermal contributions to the buoyancy forces compete. Bifurcation properties of stable and unstable…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
By large scale Monte Carlo simulations it is shown that the stable fixed point of the SO(5) theory is either bicritical or tetracritical depending on the effective interaction between the antiferromagnetism and superconductivity orders.…
In recent times out-of-time-order correlators (OTOC) have been established as a tool to understand butterfly effects, quantum information scrambling, and many-body localization. They can also be useful in determining different phases of…
A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a…
A simple random-neighbor SOC model that combines properties of the Bak-Sneppen and the relaxation oscillators (slip-stick) models is introduced. The analysis in terms of branching processes is transparent and gives insight about the…
Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are analyzed. Existence and uniqueness of…