This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of functions in an extended multifunction space (Sengupta and Ray, 2000), and the topological theory of convergence. Order, chaos, and complexity are described as dis...

This paper studies a small neural network with three neurons. First, the activation function takes the sign function. Although the network is a simple hybrid systemwith all subsystems being exponentially stable, we find that it can exhibit very complex dynamics such as limit cycles and chaos. Since the sign function is a limit case of sigmoidal functions, we find that chaos robustly exists with...

– Temperature chaos is an extreme sensitivity of the equilibrium state to a change of temperature. It arises in several disordered systems that are described by the so called scaling theory of spin glasses, while it seems to be absent in mean field models. We consider a model spin glass on a tree and show that although it has mean field behavior with replica symmetry breaking, it manifestly has...

It is recognised that tourism destinations are vulnerable to some form of crisis or disaster. Consequently, attention has long been paid to the nature and consequences of tourism crises and disasters, whilst, more recently, a number of tourism crisis management models have been proposed in the literature. Such models may, however, be criticised for their structured, linear and prescriptive appr...

It is very unusual for a mathematical or physical idea to disseminate into the society at large. An interesting example is chaos theory, popularized by Lorenz’s butterfly effect: “does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” A tiny cause can generate big consequences! Mathematicians (and non mathematicians) have known this fact for a long time! Can one adequately ...

– We demonstrate that generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)] provides a natural and reliable indicator of quantum chaotic behavior. Since generalized entanglement depends directly on a choice of preferred observables, exploring how generalized entanglement increases under dynamical evolution is possible without invoking an auxiliary coupled system or decomposin...

We discuss the appearance of cyclic and toroidal chaos in Hopfield neural networks. The theoretical results may strongly relate to investigations of brain activities performed by neurobiologists. As new phenomena, extension of chaos by entrainment of several limit cycles as well as the attraction of cyclic chaos by an equilibrium are discussed. Appropriate simulations that support the theoretic...

We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive feature of energy eigenvalues in quantum chaotic system. Chaotic dynamics in N = 2 supersymmetric Yang-Mills theory is also discussed. We demonstrate that aft...

In this paper the concept of chaos in manufacturing systems is briefly introduced and tools used in the characterization of a chaotic system are discussed. The scheduling of a simple manufacturing system, with the help of commonly used assignment rules, has been simulated first. The results have been studied with the help of phase portraits. Some conclusions have been drawn and a new method for...

“Deviner avant de démontrer! Ai-je besoin de rappeler que c’est ainsi que se sont faites toutes les découvertes importantes. Guessing before proving! Need I remind you that it is so that all important discoveries have been made? The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not bea...