We suggest a network representation of dynamical maps (such as the logistic map) on the unit interval. The unit interval is partitioned into N subintervals, which are associated with ’nodes’ of the network. A link from node i to j is defined as a possible transition of the dynamical map from one interval i, to another j. In this way directed networks more generally allow phasespace representati...

We consider a totally nonsymplectic (TNS) Anosov action of Zk which is either uniformly quasiconformal or pinched on each coarse Lyapunov distribution. We show that such an action on a torus is C∞–conjugate to an action by affine automorphisms. We also obtain similar global rigidity results for actions on an arbitrary compact manifold assuming that the coarse Lyapunov foliations are topological...

(and analogously for λmin) exists for almost all sequences and is independent of the initial (finite) choice of x(0). This result shows that, in principle, it is possible to calculate the efficiency measures discussed above. The main difference is that, although the Lyapunov exponents exist, there is no nice prescription for their calculation. The development of efficient numerical algorithms i...

Primary user emulation attack, which targets distabilizing the queuing dynamics of cognitive radio networks, is studied using game theoretic argument. The attack and defense are modeled as a stochastic game. The Nash equilibrium of the game is studied. In particular, the Lyapunov drift is considered as the reward in each round. Explicit expressions of the Nash equilibrium strategies are obtained.

We study the chaotic dynamics of a near-integrable Hamiltonian Ablowitz–Ladik lattice, which is N+2-dimensional if N is even (N+1, if N is odd) and possesses, for all N , a circle of unstable equilibria at ε = 0, whose homoclinic orbits are shown to persist for ε 6= 0 on whiskered tori. The persistence of homoclinic orbits is established through Mel’nikov conditions, directly from the Hamiltoni...

In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the approximate Markov Decision Process (MDP) approach using stochastic learning. These approaches essentially embrace most of the existing literature regarding delay...

This paper considers a fairly general model of constrained queuing networks that allows us to represent both MMBP (Markov Modulated Bernoulli Processes) arrivals and time-varying service constraints. We derive a set of sufficient conditions for throughput optimality of scheduling policies, which encompass and generalize all the results previously obtained in the field. This leads to the definit...

We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular neighborhoods of differentiable Jordan curves that are unions of finitely many segments and arcs of circles. We prove that under proper conditions on the seg...

In this paper, we study one-dimensional Newtonian filtration equation including unbounded sources with multiple delays. The existence of nonnegative non-trivial time periodic solutions will be established by the Leray-Schauder fixed point theorem based on some suitable Lyapunov functionals and some a priori estimates for all possible periodic solutions.

This paper is concerned with the control problem of biological systems modeled with Timed Continuous Petri Nets under in…nite server semantics. This work introduces two main contributions. The …rst one is a bottom-up modeling methodology that uses TCPN to represent cell metabolism. The second contribution is the control wich solves the Regulation Control Problem (RCP ) (to reach a required stat...