We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important for modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete...

We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important for modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete...

Most ecological networks are analysed as static structures, where all observed species and links are present simultaneously. However, this is over-simplified, because networks are temporally dynamical. We resolved an arctic, entire-season plant-flower visitor network into a temporal series of 1-day networks and compared the properties with its static equivalent based on data pooled over the ent...

This paper analyzes the dynamical properties of a class of hybrid systems simulators. A hybrid system is a dynamical system with a state that can both flow and jump. Its simulator attempts to generate its solutions approximately. The paper presents mild regularity conditions on the hybrid system and its simulator to guarantee that simulated solutions are close to actual solutions on compact (hy...

We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our work covers systems that admit a finite SRB measure and it also covers systems that admit an infinite SRB measure. In particular, we obtain a linear response formula for both finite and infinite SRB measures. We apply our results to interval maps with a neutral fixed p...

We give a generalization of a solution by Puri to the problem of checking emptiness in timed automata with drifting clocks for the case of automata with non-closed guards. We show that non-closed guards pose certain specific problems which cannot be handled by Puri’s algorithm, and propose a new algorithm, based on the idea of “boundary clock regions” of Alur, LaTorre and Pappas. We then give a...

Reaction networks are commonly used to model the dynamics of populations subject to transformations that follow an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs). DRNs can be seen as modeling the underlying discrete nondeterministic transitions of stochastic models of reaction networks. In that sense, a pr...

Here 0 is a two-dimensional, smooth, bounded domain, E is a positive parameter, u : R x R, R2, g : 8 R R2 is smooth, and Igl(x) = l , x E 80. Naturally we also assume the compatibility condition that u&) = g(x) on dfl. The system (l.lH1.3) can be viewed as a simplified evolutionary GinzburgLandau equation in the theory of superconductivity (141, [51, 1111, [18]). The same system also appears in...

A t ransform is introduced that maps cellular automata and discrete neural networks to dynamical systems on the unit interval. This transform is a topological conjugacy except at countably many points. In many cases, it gives rise to continuous full conjugates , in which case the transform preserves entropy. The transform also allows transfer of many dynamical properties of continuous systems t...

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncerta...