Related papers: Iterated function systems of affine expanding and …
We study synchronization of random one-dimensional linear maps for which the Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of these maps are explained using their relation with a random walk. We confirm that…
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically…
In this paper we'll give a connection between four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) of models with uncountable (i.e. $[0,1]$) set of spin values on the Cayley tree of order…
An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. The proposed technique is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions…
We study maps on the torus $\mathbb{T}^2$ that are of the form $F(x,y) = (bx, f_x(y))$, where $b\geq 2$ is an integer. We establish an open class of $C^1$-maps, with $f_x(y)$ that are typically non-monotonic in $x$, for which the Lyapunov…
The dependence of the Lyapunov exponent on the closeness parameter, $\epsilon$, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we…
A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…
We construct an integer-valued Lyapunov function $\sigma(\cdot)$ for generalized negative cyclic feedback system; and prove that $\sigma(\cdot)$ on any $\omega$-limit set which generated by Poincar\'{e} mapping of bounded solution of such…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
In the stability theory of dynamical systems, Lyapunov functions play a fundamental role. In this paper, we study the attractor-repeller pair decomposition and Morse decomposition for compact metric space in the random setting. In contrast…
We revisit the classical problem of absolute stability; assessing the robust stability of a given linear time-invariant (LTI) plant in feedback with a nonlinearity belonging to some given function class. Standard results typically take the…
We consider the typical behaviour of random dynamical systems of order-preserving interval homeomorphisms with a positive Lyapunov exponent condition at the endpoints. Our study removes any requirement for continuous differentiability save…
In this paper, we study limit behaviors of stationary measures of the Fokker-Planck equations associated with a system of ordinary differential equations perturbed by a class of multiplicative including additive white noises. As the noises…
We study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Our main object of study is the infinite matrix which encodes all the moment data of a Borel measure on R^d or C. To…
We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of…
This paper investigates the dynamical system governing the phase differences between three identical oscillators arranged symmetrically and coupled by burst interactions. By constructing a discrete Lyapunov function, we prove the existence…
In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in…
In this work we present a theoretical and numerical study of the behaviour of the maximum Lyapunov exponent for a generic coupled-map-lattice in the weak-coupling regime. We explain the observed results by introducing a suitable…
It is well know that for globally contractive autonomous systems, there exists a unique equilibrium and the distance to the equilibrium evaluated along any trajectory decreases exponentially with time. We show that, additionally, the…
Conley in \cite{Con} constructed a complete Lyapunov function for a flow on compact metric space which is constant on orbits in the chain recurrent set and is strictly decreasing on orbits outside the chain recurrent set. This indicates…