An open question in nonlinear dynamics is the relation between the Kolmogorov entropy and the largest Lyapunov exponent of a given orbit. Both have been shown to have diagnostic capability for phase transitions in thermodynamic systems. For systems with long-range interactions, the choice of boundary plays a critical role and appropriate boundary conditions must be invoked. In this work, we com...

Impulsively synchronized chaos with criterion from conditional Lyapunov exponent is often interrupted by desynchronized bursts. This is because the Lyapunov exponent can not characterize local instability of synchronized attractor. To predict the possibility of the local instability, we introduce a concept of supreme local Lyapunov exponent (SLLE), which is defined as supremum of local Lyapunov...

In this paper, the periodic, quasi periodic and chaotic responses of rotational machines with a hexagonal centrifugal governor are studied. The external disturbance is assumed as a sinusoid effect. By using the forth order Rung-Kutta numerical integration method, bifurcation diagram, largest Lyapunov exponent and Lyapunov dimension are calculated and presented to detect the critical controlling...

Modeling and analysis of future prices has been hot topic for economic analysts in recent years. Traditionally, the complex movements in the prices are usually taken as random or stochastic process. However, they may be produced by a deterministic nonlinear process. Accuracy and efficiency of economic models in the short period forecasting is strategic and crucial for business world. Nonlinear ...

Given a discrete-time random dynamical system represented by cocycle of non-singular measurable maps, we may obtain information on quantities studying the Perron–Frobenius operators associated to maps. Of particular interest is second-largest Lyapunov exponent for operators, λ2, which can tell us about mixing rates and decay correlations in system. We prove generalized theorem cocycles bounded ...

in this research the chaocity of precipitation time series in daily, weekly and monthly scales in the pole-kohneh and ghourbaghestan stations located in qarah-soo watershed is investigated. in order to reassure about the absence of stochastic behavior of the time series, method of surrogate data is applied. thereafter, the aperiodicity of the time series is investigated using power spectrum ana...

Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, 56, 2272 (1997)) is a combined result of the contracting region of the system and the finite precision in computer simulations. PACS number(s): 05.45.+b;

BACKGROUND Upright sitting is one of the first developmental motor milestones achieved by infants, and sitting postural sway provides a window into the developing motor control system. A variety of posture sway measures can be used, but the optimal measures for infant development have not been identified. METHODS We have collected sitting postural sway data from two groups of infants, one wit...

Ventilatory chaos is strongly linked to the activity of central pattern generators, alone or influenced by respiratory or cardiovascular afferents. We hypothesized that carotid atherosclerosis should alter ventilatory chaos through baroreflex and autonomic nervous system dysfunctions. Chaotic dynamics of inspiratory flow was prospectively evaluated in 75 subjects undergoing carotid ultrasonogra...