The following notes contain the proof of Lyapunov’s theorem for stability and asymptotic stability of an equilibrium point of a nonlinear system, along with applications to the proof of asymptotic stability of an equilibrium point via linearization, plus some comments on unstable equilibrium points. The material is adapted from Fornasini & Marchesini, Appunti di teoria dei sistemi (in Italian);...

A mathematical model describing the dynamical interactions of the bidirectional associative memory networks, incorporating among other things processing time delays, has been proposed in this paper. The existence and stability characteristics of the equilibrium patterns have been discussed. Results on local asymptotic stability of the equilibrium patterns have been presented. Three sets of easi...

In this paper, a five–dimensional mathematical model is proposed for the transmission dynamics of HIV/AIDS within a population of varying size. In writing the model, we have divided the population under consideration into five sub classes of susceptible, infective, pre-AIDS, AIDS related complex and that of AIDS patients. The model has two non- negative equilibria namely, a disease free and the...

In this paper fuzzy bi-directional associative memory (BAM) neural networks with constant delays are considered. Some sufficient conditions for existence and global exponential stability of unique equilibrium point are established by using fixed point theorem and differential inequality techniques. The results obtained are easily checked to guarantee existence, uniqueness and global exponential...

The interaction between benzo-15-crown-5 (B15C5), dibenzo-18-crown-6 (DB18C6), dibenzyl-daza-18crown-6 (DBzDA18C6), N-phenyl-aza-15-crown-5 (NPhA15C5) and dibenzopyridine-18-crown-6 (DBPy18C6) with π-acceptor 2,3-dichloro-5,6-dicyanobenzoquinone (DDQ) in chloroform solution was studied spectrophotometrically. The interaction of B15C5-DDQ and DB18C6-DDQ caused the formation...