Related papers: Towards Theory of Piecewise Linear Dynamical Syste…
We give an effective method for controlling the maximum number of limit cycles of some planar polynomial systems. It is based on a suitable choice of a Dulac function and the application of the well-known Bendixson-Dulac Criterion for…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded,…
A multistable system generated by a Piecewise Linear (PWL) system based on the jerky equation is presented. The systems behaviour is characterised by means of the Nearest Integer or round(x) function to control the switching events and to…
In this work, we consider a class of $n$-dimensional, $n\geq2$, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may…
Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…
We review one dimensional matrix theory and its variations, collective field theory and quantum phase space description. In the planar limit, these theories become classical and can be easily analyzed. With these descriptions, one…
We consider a class of continuous-time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces, and which include the fluid-level dynamics of the Max-Weight…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
We study the localization along a filter of several dynamical notions. This generalizes and extends similar localizations that have been considered in the literature, e.g. near 0 and near an idempotent. Definitions and basic properties of…
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 study the dynamics of piecewise conformal maps in the Riemann sphere. The normality and chaotic regions are defined and we state several results and properties of these sets. We show that the stability of these piecewise maps is related…
Using $p$-adic numbers, we partially categorize the cycles of a sizable class of polynomial dynamical systems. In turn, we prove a few results related to the non-trivial cycles of the $\textit{Collatz map}$ $\text{Col} : \mathbb{Z}_+ \to…
We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…
In this paper we study the family of planar hybrid differential systems formed by two linear centers and a polynomial reset map of any degree. We study their limit cycles and also provide examples of these hybrid systems exhibiting chaotic…
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…
We investigate sensitivity to cumulative perturbations for a few dynamical system classes of practical interest. A system is said to have bounded sensitivity to cumulative perturbations (bounded sensitivity, for short) if an additive…
It is shown how simple assumptions lead to piecewise linear behavior, which is observed in certain phase transitions.
We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…