This work investigated the stability of some Lotka-Volterra type models. We used the Liapunov method, which consists in analyzing the stability of systems of ordinary differential equations (ODE's), around the equilibrium, when submitted to perturbations in the initial conditions.

We construct the most general form of axially symmetric SU(2)-Yang-Mills fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM fields in Bianchi I model is compared with the dynamical evolution of the electromagnetic field in Bianchi I and the fully isotropic YM field in Friedmann-Robertson-Walker cosmologies. The stochastic properties of axially symmetric Bianchi I-Ein...

A local stability analysis is given for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. The standard linear stability analysis is reviewed, then it is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and of the one-leg fc-step numerical solutio...

that the linear part of Q is completely controllable1 (the vectors a, Aa, . . ., la are linearly independent) and completely observable1 (the vectors b, A'b,. (A') -1b are linearly independent), and also that the system (2) is asymptotically stable for all linear (p(ah) = uhm in the class (1). Thus, the system (2) has only one equilibrium point: Xh = XA+l = 0. 2. One wants to derive a sufficien...

The major objective of this paper is to propose a stable control rule to find a reasonable target linear and rotational velocities (v, w)'. The stability of the rule is proved through the use of a Liapunov function. The rule contains three parameters, Kx, Ky and Ke. Although any set of positive parameters makes the system stable, a condition on the parameters for the system being critically dam...

It is considered the static and dynamic analysis of an analog electrical circuit having the structure of the Hopfield neural network, the KWTA (KWinners-Take-All) network. The mathematics of circuit design and operation is discussed via two basic tools: the Liapunov function ensuring the gradient like behavior and the rational choice of the weights that stands for network training to ensure ord...