Related papers: Stability range of parameters at fixed points for …
The robustness of the stability properties of dynamical systems in the presence of unknown/adversarial perturbations to system parameters is a desirable property. In this paper, we present methods to efficiently compute and improve the…
Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of…
In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established…
Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined…
We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal…
We calculate the static critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. Summation methods lead to fixed points describing…
We call $i$ a fixed point of a given sequence if the value of that sequence at the $i$-th position coincides with $i$. Here, we enumerate fixed points in the class of restricted growth sequences. The counting process is conducted by…
The location of roots of the characteristic equation of a linear delay differential equation (DDE) determines the stability of the linear DDE. However, by its transcendency, there is no general criterion on the contained parameters for the…
We study general properties of attractors for tachyonic potential chameleon scalar-field model which possess cosmological scaling solutions. An analytic formulation is given to obtain fixed points with a discussion on their stability. The…
We study the role of multiplicative stochastic processes in the description of the dynamics of an order parameter near a critical point. We study equilibrium, as well as, out-of-equilibrium properties. By means of a functional formalism, we…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
The question of the stability of unstable states of dynamical systems that do not explicitly contain a small parameter, chaos and bifurcations in them has attracted attention ever since [1-14]. This is due to the fact that this problem…
In this paper the asymptotic stability of equilibria and periodic points of the following higher order rational difference Equation x_{n+1} =(alpha x_{n-k})/(1+x_{n}...x_{n-k}), k>=1, n=0,1,... is studied where the parameters ?alpha, betta,…
This paper presents a method to describe dynamics of an ion confined in a realistic finite range trap. We model this realistic potential with a solvable one and we obtain dynamical variables (raising and lowering operators) of this…
We show how the stability conditions for a system of interacting fermions that conventionally involve variations of thermodynamic potentials can be rewritten in terms of one- and two-particle correlators. We illustrate the applicability of…
Component graphs $\Gamma_{0}(F)$ are defined for arrays of sets $F$, and in particular for arrays of path components for Vietoris-Rips complexes and Lesnick complexes. The path components of $\Gamma_{0}(F)$ are the {\it stable components}…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…