相关论文: Dynamical behavior of a large complex system
Over fifty years ago, Robert May applied random matrix theory to show that as ecological systems grow in size, stability decreases. What emerged from this and the critique that followed was decades of what has been called the…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
Network structure strongly constrains the range of dynamic behaviors available to a complex system. These system dynamics can be classified based on their response to perturbations over time into two distinct regimes, ordered or chaotic,…
We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…
The sensitivity (i.e. dynamic response) of complex networked systems has not been well understood, making difficult to predict whether new macroscopic dynamic behavior will emerge even if we know exactly how individual nodes behave and how…
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…
We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…
Traditional methods in educational research often fail to capture the complex and evolving nature of learning processes. This chapter examines the use of complex systems theory in education to address these limitations. The chapter covers…