We study the spatial circular restricted problem of three bodies in the light of Nekhoroshev theory of stability over large time intervals. We consider in particular the Sun-Jupiter model and the Trojan asteroids in the neighborhood of the Lagrangian point L4. We find a region of effective stability around the point L4 such that if the initial point of an orbit is inside this region the orbit i...

   Scientists are interested in find out “how to use living resources without damaging the ecosystem at the same time?” from nineteen century because the living resources are limited. Thus, the harvested rate is used as the control parameters. Moreover, the study of harvested population dynamics is more realistic.    In the present paper, some predator-prey models in which two ecologically inte...

This paper deals with state feedbackH∞ control design of continuous-time switched affine systems. The main purpose is to design a set of state feedback gains together with a switching function assuring global asymptotic stability of a desired equilibrium point. The equilibrium point belongs to a set of attainable ones to be determined. Moreover, the control design must take into account a pre-s...

In this paper, the global robust asymptotic stability of the equilibrium point for a more general class of bidirectional associative memory (BAM) neural networks with variable time of impulses is addressed. Unlike most existing studies, the case of non-fix time impulses is focused on in the present study. By means of B-equivalence method, which was introduced in Akhmet (2003, 2005, 2009, 2010),...

We consider link error or physical channel error in wireless networks and propose a new ratebased congestion control scheme for wireless networks, which is based on the NUM framework developed for TCP-like congestion control model in wired networks. This scheme is distributed and can be implemented by changing the number of connections opened by one user and requires no modification to either t...

On the basis of domestic and foreign workers’ study, this paper considers the dynamic model of a duopoly price game in insurance market. In the duopoly model, we theoretically analyze the existence and stability of the Nash equilibrium point of the dynamic system, when one player or both players make a delayed decision, then stability conditions are obtained. The numerical simulation results fu...

A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-rec...

the main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $s$ to an arbitrary unitary complex banachalgebra and also $psi: s^{2}rightarrow [0,infty)$ is afunction. fur...

An unsteady nonlinear and extended version of the Moore-Greitzer model is developed to facilitate the synthesis of a quasilinear stall vibration controller. The controller is synthesised in two steps. The first step defines the equilibrium point and ensures that the desired equilibrium point is stable. In the second step, the margin of stability at the equilibrium point is tuned or increased by...

In this paper, we investigate the global dynamics of equilibrium point for delayed competitive neural networks with different time scales and discontinuous activations. Employing the Leray–Schauder alternative theorem in multivalued analysis, linear matrix inequality technique and generalized Lyapunov-like method, we obtain some new sufficient conditions ensuring the existence, uniqueness and g...