Existence and stability of periodic solutions for a class of generalized nonautonomous neural networks with distributed delays.
We give some results on the existence, uniqueness and regularity of a nonlinear evolution system. This system models the viscoelastic behaviour of unicellular marine alga Acetabularia mediterrania when the calcium concentration varies. We show (with the aid of a fixed-point theorem) that the system admits a unique local solution in time.
This paper explores the problem of delay-independent and delay-dependent stability for a class of complex-valued neutral-type neural networks with time delays. Aiming at the neutral-type neural networks, an appropriate function is constructed to derive the existence of equilibrium point. On the basis of homeomorphism theory, Lyapunov functional method and linear matrix inequality techniques, several LMI-based sufficient conditions on the existence, uniqueness and global asymptotic stability of equilibrium...
We study delay shunting inhibitory cellular neural networks without almost periodic coefficients. Some sufficient conditions are established to ensure that all solutions of the networks converge exponentially to an almost periodic function. This complements previously known results.
Since Rosenzweig showed the destabilisation of exploited ecosystems, the so called Paradox of enrichment, several mechanisms have been proposed to resolve this paradox. In this paper we will show that a feeding threshold in the functional response for predators feeding on a prey population stabilizes the system and that there exists a minimum threshold value above which the predator-prey system is unconditionally stable with respect to enrichment. Two models are analysed, the first being the classical...
In this paper, we investigate the finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures. We propose new adaptive controllers, with which we can synchronize two complex dynamical networks within finite time. Sufficient conditions for the finite-time adaptive outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to demonstrate the effectiveness and feasibility of the...
RNA viruses replicate as complex and dynamic mutant distributions. They are termed viral quasispecies, in recognition of the fundamental contribution of quasispecies theory in our understanding of error-prone replicative entities. Viral quasispecies have launched a fertile field of transdiciplinary research, both experimental and theoretical. Here we review the origin and some implications of the quasispecies concept, with emphasis on internal interactions...
A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.
We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a -pseudo almost automorphic solution. The...