Stochastic, processes can be stationary or nonstationary. They depend on the magnitude of shocks. In other words, in an auto regressive model of order one, the estimated coefficient is not constant. Another finding of this paper is the relation between estimated coefficients and residuals. We also develop a catastrophe and chaos theory for change of roots from stationary to a nonstationary one ...

Nonlinear dynamical systems exhibit a very rich class of potential modes of behavior. Among them are order, crises, and chaos, all of which can coexist within a very small range of parameters. They may serve as paradigms for the complex new world order after the end of the cold war where scenarios of delicate crisis management will replace those of plain deterrence or retaliation. In this note ...

Since Li and Yorke first gave the definition of chaos by using strict mathematical language in 1975 [1], the research on chaos has greatly influenced modern science, not just natural sciences but also several social sciences, such as economics, sociology, and philosophy. The theory of chaos convinced scientists that a simple definite system can produce complicated features and a complex system ...

This paper establishes new results for the sliding controller design for the global chaos synchronization of identical hyperchaotic Yujun systems (2010). Hyperchaotic systems are chaotic nonlinear systems having more than one positive Lyapunov exponent. Because of the complex dynamics properties of hyperchaotic system such as high capacity, high security and high efficiency, they are very usefu...

The results of extensive computations are presented to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular we follow the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos. As many as 13 period doublings are followed and used to compute the Feigenbaum number for the cascade and so enabl...

today’s organizations, in chaos, complexities, diverse, dynamic, uncertainties, and rapid and increasingly changes in technologies, markets, and life qualities, are forced to search of leaders who having the least mistakes in their decision-makings; the leaders who make the right decisions with a calculative and scrupulous sense, and serve right and suitable behaviors for guiding and leading th...

totoday’s market place is increasingly dynamic and volatile. in this area supply network issues recently have attracted a lot of attention from industrial practitioners and academics worldwide. chaos theory is the study of complex, nonlinear, dynamic systems. for chaotic systems, a tiny change in conditions may result in an enormous change in system output, whereas substantial changes in condit...