Related papers: Linear dynamical systems on graphs
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical systems (i.e., fully observable systems with no inputs),…
For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…
Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are…
We consider temporal models of rapidly changing Markovian networks modulated by time-evolving spatially dependent kernels that define rates for edge formation and dissolution. Alternatively, these can be viewed as Markovian networks with…
This paper studies the equivalence between differentiable and non-differentiable dynamics in Rn. Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo…
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
We prove that for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear…
We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, including a period doubling route to chaos. By approximating the…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
This text is a continuation to my former article "On Connectivity Spaces". It takes into account that connectivity spaces gives rise to phenomena which are essentially dynamic. In a first stage, the representation of finite connectivity…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
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…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such…