Positive periodic solution for a nonautonomous periodic model of population with time delays and impulses

In this paper, a nonautonomous periodic model of population with time delays and impulses, which arises in order to describe the control of a single population of cells, is studied. By the coincidence degree theory we obtain the conditions for the existence of periodic solution of this system.

ON THE EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS FOR HOPFIELD NEURAL NETWORK EQUATIONS WITH DELAY

Sufficient conditions are obtained for the existence, uniqueness and stability of T-periodic solutions far the Hopfield neural network equations with delay [GRAPHICS]

ON THE EXISTENCE OF PERIODIC SOLUTIONS TO HIGHER DIMENSIONAL PERIODIC SYSTEM WITH DELAY

In this paper, higher dimensional periodic systems with delay of the form x′(t)=A(t,x(t))x(t)+f(t,x(t-τ)), x′(t)= grad G(x(t))+f(t,x(t-τ)) are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive periodic solution for a logarithmic population model is proved.

PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION

A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive continuous T-periodic functions, gi(t,xi) (i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) > 0 for y>0,t, y∈R,pi(x)(i=1,2) are continuous and monotonously increasing functions, and Pi(xi)>0 for xi>0.

Periodicity in a Nonlinear Predator-prey System with State Dependent Delays

With the help of a continuation theorem based on Gaines and Mawhinscoincidence degree, easily verifiable criteria are established for the global existence of positiveperiodic solutions of the following nonlinear state dependent delays predator-prey system{dN_1(t)/dt = N_1(t)[b_1(t) - ∑ from i=1 to n of ai(t)(N_1(t-τ_i(t,N_1(t), N_2(t))))^(α_i) - ∑from j=1 to m of c_j(t)(N_2(t - σ_j(t,N1(t),N_2(t))))^(β_j)] dN_2(t)/dt = N_2(t)[-b_2(t) + ∑ fromi=1 to n of d_i(5)(N_1(t - ρ_i(t,N_1(t),N_2(t))))^(γ_i)], where a_i(t), c_j(t), d_i(t) arecontinuous positive periodic functions with periodic 】 0, b_1(t), b_2(t) are continuous periodicfunctions with periodic ω and ∫_0~ωb_i(t)dt 】 0. τ_i, σ_j, ρ_i (i = 1,2,…,m) are continuousand ω-periodic with respect to their first arguments, respectively. α_i, β_j, γ_i (i = 1,2,…,n,j = 1,2,…,m) are positive constants.

Existence and Uniqueness of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equations with Constant Delays

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form （x（t）＋Bx（t-δ））＂＋Cx＇（t）＋g（x（t-τ））=p（t）.

Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.

Existence of Positive Periodic Solutions for Nonautonomous Predator-prey Systems with Discrete and Continuously Distributed Delays

By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.

Global Existence of Positive Periodic Solutions for a Distributed Delay Competition Model

By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r 1 and r 2 are continuous ω-periodic functions in R + = [0,∞) with are positive continuous ω-periodic functions in R + = [0,∞), b i (i = 1, 2) is nonnegative continuous ω-periodic function in R + = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.

POSITIVE PERIODIC SOLUTIONS OF A CLASS OF DISCRETE TIME SYSTEM WITH DELAYS AND A FEEDBACK CONTROL

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, sufficient conditions are established for the existence of periodic solutions of a class of discrete differential system with delays and feedback control.

Multiple positive periodic solutions for a generalized delayed population model with an exploited term

In this paper, the existence of two positive periodic solutions for a generalized delayed population model with an exploited term is established by using the continuation theorem of the coincidence degree theory.

EXISTENCE OF POSITIVE PERIODIC SOLUTION TO A CLASS OF NEUTRAL DELAY COMPETITION MODEL

By means of the theory of coincidence degree, sufficient condition for the existence of positive periodic solution to certain neutral delay competition model is obtained.

PERIODIC SOLUTIONS FOR HIGHER ORDER DELAY FUNCTIONAL DIFFERENTIAL EQUATION OF NEUTRAL TYPE WITH LINEAR RESTORING TERMS

Using the theory of coincidence degree, the authors studied the existence of periodic solutions for higher order delay functional differential equations of neutral type with restoring terms and some new results for the existence of periodic solutions have been obtained.

GLOBAL EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A NEUTRAL DELAY COMPETITIVE SYSTEM

In this paper, by means of Mawhin's coincidence degree theory and somenew techniques, sufficient conditions for the global existence of positive periodicsolution to a class of neutral type competitive system with delays are obtained.

PERIODIC SOLUTIONS FOR A LINARD-TYPE EQUATION WITH DELAYS

In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Liénard-type equation with delays.

Periodic Solution to BAM-type Cohen-Grossberg Neural Network with Time-varying Delays

By using the continuation theorem of Mawhin＇s coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.

Periodicity in a “Food-limited” Population Model with Toxicants and Time Delays

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, we study the global existence of positive periodic solutions of a 'food-limited' population model with toxicants and time delays. Some new results are obtained.

POSITIVE PERIODIC SOLUTION OF AN INTEGRO-DIFFERENTIAL PREDATOR-PREY SYSTEM WITH INFINITE DELAYS

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a differential-integral predator-prey system with infinite delaywhere N1(t), N2(t) satisfy N1(t) =φ1(t), N2(t) =φ2(t), φi∈ BC((∞,0],R+φi(0)> 0,i=1,2, ∫0+∞Ki(s)ds = 1, i=1,2,3.

POSITIVE PERIODIC SOLUTION OF A PREDATOR-PREY SYSTEM WITH TIME DELAY

By using continuation theorem in coincidence degree theory, we study the existence of positive periodic solution for a delay and mutual interference predatorprey system with functional response, and obtain sufficient conditions for the existence of positive periodic solution.