Unlike evolutionary dynamics, co-evolutionary dynamics can exhibit a wide variety of complex regimes. This has been confirmed by numerical studies e.g. in the context of Evolutionary Game Theory (EGT) and population dynamics of simple two-strategy games with various types of replication and selection mechanisms. Using the framework of shadowing lemma we study to what degree can such infinite po...

We present some fixed point results for mappings which satisfy Hardy–Rogers rational type, quasicontraction type, weak contraction type and generalized fψ type cyclic conditions in 0-complete partial metric spaces. Presented results generalize or improve many existing fixed point theorems in the literature. To demonstrate our results, we give throughout the paper some examples. One of the possi...

We prove that for any closed manifold of dimension 3 or greater there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one. Additionally, we show that the stabilization of the shadowing closure of a hyperbolic set is an intrinsic property for premaximality. Lastly, we review some results due to Anosov that concern premaximality.

Simulations play a crucial role in the modern study of physical systems. A major open question for long dynamical simulations of physical processes is the role of discretization and truncation errors in the outcome. A general mechanism is described that can cause extremely small noise inputs to result in errors in simulation statistics that are several orders of magnitude larger. A scaling law ...

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. well-posedness the problem and limit shadowing property are also discussed. Some examples given order support our results, last part considers some applications main results. first section devoted study existence a solution boundary value problem. In second section, we solutions fra...

Let $G$ be a countable monoid and let $A$ an Artinian group (resp. module). $\Sigma \subset A^G$ closed subshift which is also subgroup submodule) of $A^G$. Suppose that $\Gamma$ finitely generated consisting pairwise commuting cellular automata \to \Sigma$ are homomorphisms groups modules) with binary operation given by composition maps. We show the valuation action on $\Sigma$ satisfies natur...

Abstract In this article we study dynamical behaviour of generic Lebesgue measure-preserving interval maps. We show that for each k ⩾ 1 the set periodic points period at least is a Cantor Hausdorff dimension zero and upper box one. Moreover, obtain analogous results also in context circle Furthermore, building on former results, there dense collection transitive maps whose have full measure pos...