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The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
A new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with computer- assisted computations. As an…
The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further…
The classical Lorenz lowest order system of three nonlinear ordinary differential equations, capable of producing chaotic solutions, has been generalized by various authors in two main directions: (i) for number of equations larger than…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
It has been shown that the discrete one dimensional gravity model of traffic flow dynamics exhibits temporal chaotic behavior
Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show…
The model system manifesting phenomena peculiar to complex analytic maps is offered. The system is a non-autonomous ring cavity with nonlinear elements and filters,
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium…
Generalized synchronization of chaos is a type of cooperative behavior in directionally-coupled oscillators that is characterized by existence of stable and persistent functional dependence of response trajectories from the chaotic…
A review of some recent results and ideas about the expected behaviour of large chaotic systems and fluids.
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…
In this paper, the familiar problems of free-fall motion and simple harmonic motion (SHM) are combined. The novel composite system passes from regular to chaotic behavior for increasing values of energy $E$. This system is a suitable…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…
Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the…
The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…