Related papers: Attractor Basins in Concurrent Systems
This paper presents a new chaotic system having four attractors, including two fixed point attractors and two symmetrical chaotic strange attractors. Dynamical properties of the system, viz. sensitive dependence on initial conditions,…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors of the convergence process), in the generalized H\'{e}non-Heiles system (GHH). The evolution of the position as well…
Fundamental limits to predictability are central to our understanding of many physical and computational systems. Here we show that, despite its remarkable capabilities, deep learning exhibits such fundamental limits rooted in the fractal,…
In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets…
Plans often change due to changes in the situation or our understanding of the situation. Sometimes, a feasible plan may not even exist, and identifying such infeasibilities is useful to determine when requirements need adjustment. Common…
We use simple equations in order to compare the basins of attraction on the complex plane, corresponding to a large collection of numerical methods, of several order. Two cases are considered, regarding the total number of the roots, which…
Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…
We extend a recently introduced class of exactly solvable models for recurrent neural networks with competition between 1D nearest neighbour and infinite range information processing. We increase the potential for further frustration and…
Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we…
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
In the modelling and analysis of large, real systems, the main problem in their efficient processing is the size of the global model. One of the popular approaches that address this issue is the decomposition of such global model into much…
Physical systems experience nonlinear disturbances which have the potential to disrupt desired behavior. For a particular disturbance, whether or not the system recovers from the disturbance to a desired stable equilibrium point depends on…
We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e.…
Real-world systems often evolve on different timescales and possess multiple coexisting stable states. Whether or not a system returns to a given stable state after being perturbed away from it depends on the shape and extent of its basin…
We propose a new method that takes advantage of structural reductions to accelerate the verification of reachability properties on Petri nets. Our approach relies on a state space abstraction, called polyhedral abstraction, which involves a…
Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize the riddled basin using the uncertainty…
Systems with many stable configurations abound in nature, both in living and inanimate matter. Their inherent nonlinearity and sensitivity to small perturbations make them challenging to study, particularly in the presence of external…
Vector Addition Systems (VAS), aka Petri nets, are a popular model of concurrency. The reachability set of a VAS is the set of configurations reachable from the initial configuration. Leroux has studied the geometric properties of VAS…
This paper contains introductory material on Petri nets and Groebner basis theory and makes some observations on the relation between the two areas. The aim of the paper is to show how Groebner basis procedures can be applied to the problem…