Different types of chaotic flow are possible in the 3-dimensional state spaces of two simple nonlinear differential equations. The first equation consists of a 2-variable, double-focus subsystem complemented by a linearly coupled third variable. It produces at least three types of chaos: Lorenzian chaos, "sandwich" chaos, and "horseshoe" chaos. Two figure 8-shaped chaotic regimes of the latter ...

in purpose of this paper is to discuss the occurance of bifurcation and chaos in nonlinear systems in general, and the pearl-reed model whi.ch has been used for representing the lynamical behavior of the petroleum resources in particular. based on this investigation, it is shown that the observed tluctuations in the petroleum market can be erplained by its interral dynamics and the increase in ...

It is shown that evolution of wave functions in nonintegrable quantum systems is unpredictable for a long time T because of rapid growth of number of elementary computational operations O(T ) ∼ Tα. On the other hand, the evolution of wave functions in integrable systems can be predicted by the fast algorithms O(T ) ∼ (log2T )β for logarithmically short time and thus there is an algorithmic ”com...

This paper focuses on the adaptivemodified hybrid function projective synchronization with complex function transformationmatrix (CMHFPS) for different dimensional chaotic (hyperchaotic) systemswith complex variables and unknown complex parameters. The chaotic systems are considerably different from those in the existing closely related literature. Moreover, the transformation matrix in this ty...

Let (N) denote a mean-eld measure with potential F. Asymptotic independence properties of the measure (N) are investigated. In particular, with H(j) denoting relative entropy, if there exists a unique non{degenerate minimum of H(j) ? F(), then propagation of chaos holds for blocks of size o(N). Certain degenerate situations are also studied. The results are applied for the Langevin dynamics of ...

Risk factors are generally defined and assigned to road networks, as constant measures in hazmat routing problems. In fact, they may be dynamic variables depending on traffic volume, weather and road condition, and drivers' behavior. In this research work, risk factors are defined as dynamic variables using the concept of chaos theory. The largest Lyapunov exponent is utilized to determine the ...

The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in the paper. In order to suppress the irregular chaotic motion, an optimal backstepping controller is designed. The backstepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the syste...

The discovery of fifth nonlinear region of operation i.e. quasi–chaos is confirmed in this paper after its recently reported two observations in loss and pumpmodulated Erbium doped fiber ring lasers.Quasi-chaos is apparently chaos but its time and physical phase space trajectories actually converge instead of diverging, even for widely separated initial conditions once the system numerical mode...

We study numerically statistical distributions of sums of orbit coordinates, viewed as independent random variables in the spirit of the Central Limit Theorem, in weakly chaotic regimes associated with the excitation of the first (k = 1) and last (k = N) linear normal modes of the Fermi-Pasta-Ulam-α system under fixed boundary conditions. We show that at low energies (E = 0.19), when the k = 1 ...

Melnikov's method for nding necessary conditions for homoclinic chaos is extended to a class of stochastically forced multi-degree of freedom nonlinear systems. The stochastic forcing induces a stochastic Melnikov process, and simple zeros of this process imply transversal intersection of appropriate stable and unstable manifolds. This process can also provide information on probabilities of es...