[PDF] Top 20 Global attractivity without stability for Liénard type systems

... Abstract. We are concerned with some conditions such as the trivial solution of a planar system of differential equations (including the Liénard system) that is globally attractive but not stable. We emphasize the ... See full document

... In this paper, we propose and study a nonautonomous modified Leslie-Gower predator- prey model with Holling-type II schemes and a prey refuge. We first obtain a set of suffi- cient conditions which ensure the ... See full document

... Fractional calculus is a generalization of the ordinary differentiation and integration to arbitrary non-integer order. The subject is as old as the differential calculus and it has been developed up to nowadays (see ... See full document

... the stability prop- erty of the mutualism model, Yang, Xie, and Chen [] showed that some additional con- dition should be added to ensure the global stability of the ...the stability ... See full document

... derived. The analysis in [21] proceeds along the classical lines of constructing an integro–differential equation resembling the forced pendulum equation and, subsequently, showing that the SMIB system is almost globally ... See full document

... In this paper, we deal with a discrete Lotka-Volterra predator-prey model with time-varying delays. For the general non-autonomous case, sufficient conditions which ensure the permanence and global stability ... See full document

... Yet, in spite of these efforts, due to the complexity of the dynamics of a power system—even at the individual component level—many basic questions remain open. There- fore, typical stability analysis (and also ... See full document

... The paper is arranged as follows. We will investigate the extinction, partial survival and persistency of system (1.4) in the next section. In Sect. 3, we investigate the global stability property of the ... See full document

... known, stability is one of the main properties of neural networks, which is a crucial feature in the design and hardware implementation of neural ...the global asymptotic or exponential stability of ... See full document

... SIS models are used for diseases where there is no immunity, then once that infected people recover, they become susceptible again. Hence his name; since the progression of the disease, from the point of view of an ... See full document

... where the nonlinear term g has a singularity of repulsive type. The author showed that Eq. (1.3) has at least one periodic solution by applications of coincidence degree theory. Zhang’s work has attracted the ... See full document

... almost global stability of an ...almost global stability, in the same way as a common Lyapunov function implies global stability for nonlinear switched ...the global ... See full document

... uniformly global attractivity and utimately posivity are the main qualitative behaviour of solution of the nonlinear integral equations and we have shown existence and the above qualitative behaviour of ... See full document

... In this paper we study an attraction–repulsion chemotaxis system with a free boundary in one space dimension. First, under some conditions, we investigate existence, uniqueness and uniform estimates of the global ... See full document

... Now, the question is how to study the periodic problem of equation (.) under the condition of weak singularity   g(s)ds > – ∞ . Motivated by this, the purpose of this paper is to investigate the existence of ... See full document

... Hakl, R, Torres, P, Zamora, M: Periodic solutions of singular second order differential equations: upper and lower functions.. Lazer, AC, Solimini, S: On periodic solutions of nonlinear d[r] ... See full document

... problem driven by the scalar p-Laplacian with a nonsmooth potential via the degree map; they proved the existence of at least three distinct nontrivial solutions, two of which have a constant sign. In Gaines and Mawhin’s ... See full document

... [5] Liu, Q., Zu, L. and Jiang, D.Q. (2016) Dynamics of Stochastic Predator-Prey Models with Holling II Functional Response. Communications in Nonlinear Science and Numerical Simulation , 37, 62-76. ... See full document

... The rest of the paper is arranged as follows. With the help of several useful lemmas, we will prove Theorem . in Section . Two examples together with their numeric simula- tions are presented in Section  to show the ... See full document

... During the last decades, many scholars investigated the dynamic behaviors of the cooper- ative system, or mutualism model, see [–] and the references cited therein. Specially, in a series of their studies, Chen and ... See full document