Finite-time and finite-size Lyapunov exponents are related concepts that have been used for the purpose of identifying transport structures in time-dependent flow. The preference for one or the other concept seems to be based more on a tradition within a scientific community than on proven advantages. In this study, we demonstrate that with the two concepts highly similar visualizations can be ...

In this contribution we report on a transition to high-dimensional chaos through three-frequency quasiperiodic behavior. The resulting chaotic attractor has a one positive and two null Lyapunov exponents. The transition occurs at the point at which two symmetry related threedimensional tori merge in a crisis-like bifurcation. The route can be summarized as: 2D torus → 3D torus→ high-dimensional...

| The problem of synchronization of coupled chaotic systems is considered. The notion of local transversal Lyapunov exponents is introduced. We show that they can be successfully used in investigations of the synchronization properties. The technique is illustrated with computer simulations.

In this article, we propose a class of high-order stochastic partial differential equations (SPDEs) for spatial dimensions d ≤ 5 which might be called high-order stochastic Anderson models. This class of the equations is perturbed by a space-time white noise when d ≤ 3 and by a space-correlated Gaussian noise when d = 4, 5. The objectives of this article are to get some estimates on the Lyapuno...

The paper discusses nonautonomous discrete Lotka–Volterra type n-species competitive systems with pure-delays and feedback controls. New sufficient conditions for which a part of the n-species remains permanent and others is driven to extinction are established by using the method of multiple discrete Lyapunov functionals and introducing new analysis technique. Our results show that the feedbac...

Lyapunov exponents (LEs) are key indicators of chaos in dynamical systems. In general relativity the classical definition of LE meets difficulty because it is not coordinate invariant and spacetime coordinates lose their physical meaning as in Newtonian dynamics. We propose a new definition of relativistic LE and give its algorithm in any coordinate system, which represents the observed changin...

The delay guarantee is a challenge in wireless sensor networks (WSNs), where energy constraints must be considered. The coexistence of renewable energy and electricity grid is expected as a promising energy supply manner for WSNs to remain function for a potentially infinite lifetime. In this paper, we address cross-layer control to guarantee worse case delay for Heterogeneous Powered (HP) WSNs...

Economic model predictive control (EMPC) has been a popular topic in the recent chemical process control literature due to its potential to improve process profit by operating a system in a time-varying manner. However, time-varying operation may cause excessive wear of the process components such as valves and pumps. To address this issue, input magnitude constraints and input rate-of-change c...

We provide partial Lyapunov characterizations for a recently proposed generalization of input-to-state and integral input-to-state stability (ISS and iISS, respectively). This generalization relies on the notion of stability with respect to two measures originally introduced by Movchan [1960]. We show that the two classical Lyapunov characterizations of ISS-type properties, i.e., decrease condi...

Lyapunov drift is a powerful tool for optimizing stochastic queueing networks subject to stability. However, the most convenient drift conditions often provide results in terms of a time average expectation, rather than a pure time average. This paper provides an extended drift-plus-penalty result that ensures stability with desired time averages with probability 1. The analysis uses the law of...