Related papers: Dynamical systems with a prescribed attracting set…

We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orbits of a given dynamical system. We develop theory for it…

We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…

In the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are…

Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…

In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for…

In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…

This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical…

We examine the feasibility of predicting and subsequently managing the future evolution of a Complex Adaptive System. Our archetypal system mimics a competitive population of mechanical, biological, informational or human objects. We show…

This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…

Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…

Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems such as gradient and metriplectic systems with constraints.…

This study covers an analytical approach to calculate positively invariant sets of dynamical systems. Using Lyapunov techniques and quantifier elimination methods, an automatic procedure for determining bounds in the state space as an…

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…

We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…

It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using either a presymplectic or a Poisson approach. The…

We introduce deterministic concurrent systems as a subclass of concurrent systems. Deterministic concurrent system are "locally commutative" concurrent systems. We prove that irreducible and deterministic concurrent systems have a unique…

We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant $\delta$-scrambled set for some $\delta>0$ if…