We study resonances of chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response. We find that resonant forcing functions complement the separation of nearby trajectories, in that the product of the displacement of nearby trajectories and the resonant forcing is a conserved quantity. As a consequence, the resonant functi...

Structural changes were the main focus of many studies in recent years. Changes which alter the socio-economic status of a nation from deprived and traditional nature to a developed and modern one. The main hypothesis of this study is that, the economic development does not occur through a regular flow of life (linear fashion), and without resilience, but it certainly needs to pass through a mo...

For targeted prevention of falls, it is necessary to identify individuals with balance impairments. To test the sensitivity of measures of variability, local stability and orbital stability of trunk kinematics to balance impairments during gait, we used galvanic vestibular stimulation (GVS) to impair balance in 12 young adults while walking on a treadmill at different speeds. Inertial sensors w...

We construct an approximation for the moment Lyapunov exponent, the asymptotic growth rate of the moments of the response of a two-dimensional linear system driven by real or white noise. A perturbation approach is used to obtain explicit expressions for these exponents in the presence of small intensity noise. As an example, we study the moment stability of the stationary solution of nonlinear...

In our study, the nonlinear dynamics of mitral valve Doppler signals from 32 healthy and 28 patients with mitral valve stenosis was evaluated using by the computation of Lyapunov exponents, correlation dimension values and surrogate data analysis. Two chaotic features are compared for healthy and patient subjects. It was found that the largest Lyapunov exponent and correlation dimension values ...

Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question of whether strong and weak chaos can be identified fro...

Results are reported concerning the transition to chaos in random dynamical systems. In particular, situations are considered where a periodic attractor coexists with a nonattracting chaotic saddle, which can be expected in any periodic window of a nonlinear dynamical system. Under noise, the asymptotic attractor of the system can become chaotic, as characterized by the appearance of a positive...

For any N ×N monodromy matrix we define the Lyapunov function, which is analytic on an associated N-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov function for the Hill operator. The Lyapunov function has (real or complex) branch points, which we call resonances. We determine the asymptotics of the periodic, anti-periodic spectrum and of...

In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and statitical independence of the constituent parts. An example of interacting Bernoulli units is used to illustrate the nature of these invariants. 1 Conditional exp...

We show that there exists a C∞ volume preserving diffeomorphism P of a compact smooth Riemannian manifold M of dimension 4, which is close to the identity map and has nonzero Lyapunov exponents on an open and dense subset G of not full measure and has zero Lyapunov exponent on the complement of G. Moreover, P |G has countably many disjoint open ergodic components.