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A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
It was discovered recently that frictional granular materials can exhibit an important mechanism for instabilities, i.e the appearance of pairs of complex eigenvalues in their stability matrix. The consequence is an oscillatory exponential…
Network of nonlinear dynamical elements often show clustering of synchronization by chaotic instability. Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis of partially ordered…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
We investigate the phenomenon of parametric instability in discrete models of spatiotemporally modulated materials. These materials are celebrated in part because they exhibit nonreciprocal transmission characteristics. However, parametric…
The optical properties of materials are strongly influenced by disorder. Control of disorder in photonic materials can unveil interesting optical properties. We have found an engineered photonic structure for which the average light…
Highly connected recurrent neural networks often produce chaotic dynamics, meaning their precise activity is sensitive to small perturbations. What are the consequences for how such networks encode streams of temporal stimuli? On the one…
Although internal gravity waves are generally recognized as an important mechanism to distribute energy through the atmosphere, their dynamics near the instability is only partially understood to date. Many types of instabilities, notably…
We describe the dynamics of a stream of equally spaced macroscopic particles in orbit around a central body (e.g. a planet or star). A co-orbital configuration of small bodies may be subject to gravitational instability, which takes the…
We study relativistic scattering when one only has access to a subset of the particles, using the language of quantum measurement theory. We give an exact, non-perturbative formula for the von Neumann entanglement entropy of an apparatus…
A nonlinear small-world network model has been presented to investigate the effect of nonlinear interaction and time delay on the dynamic properties of small-world networks. Both numerical simulations and analytical analysis for networks…
We study diffusion in a one-dimensional periodic array of scatterers modeled by a simple map. The chaotic scattering process for this map can be changed by a control parameter and exhibits the dynamics of a crisis in chaotic scattering. We…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
We study a coupled dynamics of a network and a particle system. Particles of density $\rho$ diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics…
Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general…
Dynamical behaviors of a dissipative particle in a periodic potential subject to chaotic noise are reported. We discovered a macroscopic symmetry breaking effect of chaotic noise on a dissipative particle in a multi-stable systems emerging,…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
We investigate beam diffraction and spatial modulation instability of coherent light beams propagating in the non-paraxial regime in a nonlinear Kerr medium. We study the instability of plane wave solutions in terms of the degree of…