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The authors of this paper examine uniformly asymptotically stability (UAS). uniformly boundedness (UB). ultimately uniformly boundedness (UUB) and existence of periodic solutions (EPSs) of certain nonlinear delay differential equations (DDEs) of third order with multiple constant delays. They prove two results and give a corollary on these properties of solutions. The main results of this paper have sufficient conditions and the technique of the proofs for these results is based on construction of a proper Lyapunov- KrasovskiT function (LKF). This paper has novel results to the theory of DDEs of third order and fills some gaps related to the mentioned concepts. [ABSTRACT FROM AUTHOR]

In this work we analyze the stability properties of a complex, strongly nonlinear model of delay-differential equations with multiple delays, for cell evolution in leukemia. The model includes the action of the immune system. The competition on space between healthy and leukemic cell populations is taken into consideration. Three types of division that a stem-like cell can undergo, asymmetric division, self-renew and differentiation are also considered. Numerical results and simulations are discussed in relation to clinical implications of the proposed model. [ABSTRACT FROM AUTHOR]