Partial characterization of the global attractor of the equation .
We study the coexistence of multiple periodic solutions for an analogue of the integrate-and-fire neuron model of two-neuron recurrent inhibitory loops with delayed feedback, which incorporates the firing process and absolute refractory period. Upon receiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits a spike with a pattern-related delay, in addition to the synaptic delay. We present a theoretical framework to view...
The aim of this paper is to study periodic solutions of Marchuk's model, i.e. the system of ordinary differential equations with time delay describing the immune reactions. The Hopf bifurcation theorem is used to show the existence of a periodic solution for some values of the delay. Periodic dynamics caused by periodic immune reactivity or periodic initial data functions are compared. Autocorrelation functions are used to check the periodicity or quasiperiodicity of behaviour.
In this paper, we study the existence of periodic solutions to a class of functional differential system. By using Schauder's fixed point theorem, we show that the system has aperiodic solution under given conditions. Finally, four examples are given to demonstrate the validity of our main results.
By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form
We consider first order neutral functional differential equations with multiple deviating arguments of the form . By using coincidence degree theory, we establish some sufficient conditions on the existence and uniqueness of periodic solutions for the above equation. Moreover, two examples are given to illustrate the effectiveness of our results.
By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for th order delay differential equations with damping terms . Some new results on the existence of periodic solutions of the investigated equation are obtained.