Related papers: Regularities in the dynamics and development of th…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
We consider a contracting universe and its transition to expansion through the big bang singularity with a time varying equation of state $w$, where $w$ approaches $1$ as the universe contracts to the big bang. We show that this singularity…
Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…
Although very large wars remain an enduring threat in global politics, we lack a clear understanding of how some wars become large and costly, while most do not. There are three possibilities: large conflicts start with and maintain intense…
The global stability of laminar axisymmetric low-density jets is investigated in the low Mach number approximation. The linear modal dynamics is found to be characterised by two features: a stable arc branch of eigenmodes and an isolated…
In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…
The growth of business firms is an example of a system of complex interacting units that resembles complex interacting systems in nature such as earthquakes. Remarkably, work in econophysics has provided evidence that the statistical…
A new type of asymptotic behavior in a game dynamics system is discovered. The system exhibits behavior which combines chaotic motion and attraction to heteroclinic cycles; the trajectory visits several unstable stationary states repeatedly…
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic…
During a financial crisis, the capital markets network frequently exhibits a high correlation between returns. We developed a network analysis framework based on daily returns from 42 countries to determine systemic stability. Our network…
The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale…
Armed conflict exhibits regularities beyond known power law distributions of fatalities and duration over varying culture and geography. We systematically cluster conflict reports from a database of $10^5$ events from Africa spanning 20…
Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In physical systems order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing…
Societal complexity may be at a historical peak. Distinct from entropy, complexity tends to rise as systems move away from order, crest at an intermediate state, and decline as entropy continues increasing. The use of a thermodynamic…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture,…
Globalization processes interweave economic structures at a worldwide scale, trade playing a central role as one of the elemental channels of interaction among countries. Despite the significance of such phenomena, measuring economic…
The topology of social networks can be understood as being inherently dynamic, with edges having a distinct position in time. Most characterizations of dynamic networks discretize time by converting temporal information into a sequence of…
In this work we study the Boolean Networks of different geometric shape and lattice organization. It was revealed that no only a spatial shape but also type of lattice are very important for definition of the structure-dynamics relation.…
Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…