Qualitative analysis of nonlinear quasi-monotone dynamical systems described by functional-differential equations

This paper discusses properties related to the stability of a nonlinear quasi-monotone dynamical system described by a functionaldifferential equation . Specially, mathematical conditions which guarantee the same qualitative behavior inherent in a nonlinear off-diagonally monotone dynamical system are discussed. We first consider the basic properties of solutions: lower and upper bound preservation and ordering preservation of solutions. By using these properties, we estimate the trajectory. behavior by means of a partial ordering relation, and derive the following results: If is independent of , and is a constant input, then every bounded solution converges to a unique equilibrium point under some natural conditions. In addition, if is a nonlinear functional with separate variables, then every solution converges to under the same conditions; If and are periodic and have the same period , then, under certain natural conditions, there is a -periodic solution , and every solution converges to it if it is a unique -periodic solution.