Comments on “Asymptotically stable equilibrium points in new chaotic systems”

On the stable equilibrium points of gradient systems

This paper studies the relations between the local minima of a cost function f and the stable equilibria of the gradient descent flow of f . In particular, it is shown that, under the assumption that f is real analytic, local minimality is necessary and sufficient for stability. Under the weaker assumption that f is indefinitely continuously differentiable, local minimality is neither necessary...

Delay-Dependent Robust Asymptotically Stable for Linear Time Variant Systems

In this paper, the problem of delay dependent robust asymptotically stable for uncertain linear time-variant system with multiple delays is investigated. A new delay-dependent stability sufficient condition is given by using the Lyapunov method, linear matrix inequality (LMI), parameterized first-order model transformation technique and transformation of the interval uncertainty in to the norm ...

Simple Chaotic flows with One Stable equilibrium

It is widely recognized that mathematically simple systems of nonlinear differential equations can exhibit chaos. With the advent of fast computers, it is now possible to explore the entire parameter space of these systems with the goal of finding parameters that result in some desired characteristics of the system. Recently there has been increasing attention to some unusual examples of such s...

Horseshoes in a Chaotic System with only One Stable equilibrium

Fixed points for total asymptotically nonexpansive mappings in a new version of bead ‎space‎

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...