In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving non-smooth convex objective functions. Based on the Yosida regularization of the subdifferential operators involved in the system, we obtain the existence of strong global trajectories. We prove a descent property for each objective function, and the conve...

Stability plays an important role in the theory of dynamical systems and control. It characterizes the property of an unperturbed trajectory that all perturbed trajectories starting nearby stay nearby: small perturbations cause only small changes in the system behavior. The most important concept of stability has bee introduced by the Russian mathematician A. M. Lyapunov in 1892. Based on his f...

A new neuron activation function based on a property found in physical systems--hysteresis--is proposed. We incorporate this neuron activation in a fully connected dynamical system to form the hysteretic Hopfield neural network (HHNN). We then present an analog implementation of this architecture and its associated dynamical equation and energy function.We proceed to prove Lyapunov stability fo...

Abstract. We study weak mixing of all orders for asymptotically abelian weakly mixing state preserving C*-dynamical systems, where the dynamics is given by the action of an abelian second countable locally compact group which contains a Følner sequence satisfying the Tempelman condition. For a smaller class of groups (which include Z and R) this is then used to show that an asymptotically abeli...

We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a novel graph-theoretic feature consisting of a particularly disordered cycle structure. Disregarding efficiency of control functions, but choosing subfamilies...

In this paper, the dynamics of multicellular chopper are considered. The model is described by a continuous time three--dimensional autonomous system. Some basic dynamical properties such as Poincar'e mapping, power spectrum and chaotic behaviors are studied. Analysis results show that this system has complex dynamics with some interesting characteristics.

This paper presents the effect of preload on nonlinear dynamic behavior of a rigid rotor supported by two-lobe aerodynamic noncircular journal bearing. A finite element method is employed to solve the Reynolds equation in static and dynamical states and the dynamical equations are solved using Runge-Kutta method. To analyze the behavior of the rotor center in the horizontal and vertical directi...

UNLABELLED It is acknowledged that the presence of positive or negative circuits in regulatory networks such as genetic networks is linked to the emergence of significant dynamical properties such as multistability (involved in differentiation) and periodic oscillations (involved in homeostasis). Rules proposed by the biologist R. Thomas assert that these circuits are necessary for such dynamic...

It is acknowledged that the presence of positive or negative circuits in regulatory networks such as genetic networks is linked to the emergence of significant dynamical properties such as multistability (involved in differentiation) and periodic oscillations (homeostasis). Rules proposed by the biologist R. Thomas assert that these circuits are necessary for such dynamical properties. These ru...