I ■V *■ • • • iV*TC | V j j J j (1.1) x'=/(x) in which f(x) is of class C1 on En. Let J(x) = (df/dx) denote the Jacobian matrix of /and let H(x) = (J+J*)/2 be the symmetric part of J(x). One of the results of [2] is to the effect that if (1.2) /(0) = 0 and (1.3) H(x) is negative definite (for fixed x ^ 0), then x = 0 is a globally asymptotically stable solution of (1.1); i.e., every solution x ...

Let (M, g) be an asymptotically locally hyperbolic (ALH) manifold which is the interior of a conformally compact manifold and (∂M, [γ]) its conformal infinity. Suppose that the Ricci tensor of (M, g) dominates that of the hyperbolic space and that its scalar curvature satisfies a certain decay condition at infinity. If the Yamabe invariant of (∂M, [γ]) is non-negative, we prove that there exist...

We construct families of asymptotically locally hyperbolic Riemannian metrics with constant scalar curvature (i.e., time symmetric vacuum general relativistic initial data sets negative cosmological constant), prescribed topology apparent horizons and the conformal boundary at infinity, controlled mass. In particular we obtain new classes solutions

this paper investigates the stability analysis of fuzzy relational dynamic systems. a new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a first-order fuzzy relational dynamic system with sumproduct fuzzy composition. this approach is also investigated for other types of fuzzy relational composit...

In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system i...

In sub-Saharan Africa, the model of care for people who are living with HIV/AIDS has changed from hospital care to home-based care. In this paper, a mathematical model describing the dynamics of HIV transmission, hospitalization, and home-based care is constructed and analysed. The model reproduction number R(e) is determined and discussed. The equilibria are determined and analysed in terms of...

A quadratic Lyapunov function is demonstrated for the non-invertible planar Ricker map (x,y)↦(xer−x−αy,yes−y−βx) which shows that α,β>0, and 0<r,s≤2 all orbits of converge to a fixed point. We establish 0<r, s<2, whenever positive equilibrium exists locally asymptotically stable, it globally stable (i.e. attracts (0,∞)2). Our approach bypasses improves on methods rely monotonicity, require 0<r,...