Related papers: Dynamical behavior of a large complex system

An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can…

A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…

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…

This is a note on some results of the central limit theorem for deterministic dynamical systems. First, we give the central limit theorem for martingales, which is a main tool. Then we give the main results on the central limit theorem in…

The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their…

We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well…

We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…

Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive…

We analyse large deviations of the dynamical activity in one-dimensional systems of diffusing hard particles. Using an optimal-control representation of the large-deviation problem, we analyse effective interaction forces which can be added…

Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…

Understanding the dynamical behavior of complex systems is of exceptional relevance in everyday life, from biology to economy. In order to describe the dynamical organization of complex systems, existing methods require the knowledge of the…

We consider large deviations of the dynamical activity in the East model. We bias this system to larger than average activity and investigate the structure that emerges. To best characterise this structure, we exploit the fact that there…

Logical modeling is a powerful tool in biology, offering a system-level understanding of the complex interactions that govern biological processes. A gap that hinders the scalability of logical models is the need to specify the update…

Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels…

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…