Related papers: Self-Organized Criticality and Punctuated Equilibr…
I review the concept of self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales. Several exact results are…
My goal is to study the dynamics of the Universe from a relational perspective based on the happening of events in temporal relation to each other and their respective points of reference. Accordingly, the flow of time was modeled as the…
Atmospheric flows exhibit selfsimilar fluctuations on all scales(space-time) ranging from climate(kilometers/years) to turbulence(millimeters/seconds) manifested as fractal geometry to the global cloud cover pattern concomitant with inverse…
Topological concepts have been employed to understand the ground states of many strongly correlated systems, but it is still quite unclear if and how topology manifests itself in the relaxation dynamics. Here we uncover emergent topological…
The sustainability conditions for the market participants with a different ownership model were also determined. It was revealed, that the nonlinear form of the equations describing the market behavior with the prevailing private capital,…
Bursty dynamics characterizes systems that evolve through short active periods of several events, which are separated by long periods of inactivity. Systems with such temporal heterogeneities are not only found in nature but also include…
We present the dynamical analysis for interacting quintessence, considering linear cosmological perturbations. Matter perturbations improve the background analysis and viable critical points describing the transition of the three…
Disordered systems are an important class of models in statistical mechanics, having the defining characteristic that the energy landscape is a fixed realization of a random field. Examples include various models of glasses and polymers.…
We introduce a new and robust approach for characterizing spatially and temporally heterogeneous behavior within a system based on the evolution of dynamic fuctuations once averaged over different space lengths and time scales. We apply it…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
Recent research on the non-stationary nature of the dynamics of complex systems is reviewed through three specific models. The long time dynamics consists of a slow, decelerating but spasmodic release of generalized intrinsic strain. These…
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…
We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
Atmospheric flows exhibit fluctuations of all scales (space -time) ranging from turbulence (millimeters-seconds) to climate (thousands of kilometers-years). The apparently random fluctuations however exhibit long-range spatio-temporal…
Biological activities are often seen entrained onto the day-night and other celestial mechanical cycles (e.g., seasonal and lunar), but studies on the origin of life have largely not accounted for such periodic external environmental…
Chaos is usually referred to the sensitivity to initial conditions in which the nonlinearity plays a crucial role. Beyond such a mathematical description, the understanding of the underlying physical origin of the chaos is still not very…
The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the…
Classically chaotic systems relax to coarse grained states of equilibrium. Here we numerically study the quantization of such bounded relaxing systems, in particular the quasi-periodic fluctuations associated with the correlation between…