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...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.展开更多
Sufficient conditions are obtained for the existence, uniqueness and stability of T-periodic solutions far the Hopfield neural network equations with delay [GRAPHICS]
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 suffic...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.展开更多
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 c...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.展开更多
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...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.展开更多
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 o...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).展开更多
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-autonomou...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.展开更多
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...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.展开更多
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 &l...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 <SUB>1</SUB> and r <SUB>2</SUB> are continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞) with are positive continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous ω-periodic function in R <SUB>+</SUB> = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.展开更多
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 d...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.展开更多
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.
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.
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 th...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.展开更多
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 ...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.展开更多
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.
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 stab...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.展开更多
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...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.展开更多
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-integra...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.展开更多
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 ...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.展开更多
文摘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.
文摘Sufficient conditions are obtained for the existence, uniqueness and stability of T-periodic solutions far the Hopfield neural network equations with delay [GRAPHICS]
文摘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.
基金The project is supported by Youth Project Foundation of Hubei Education Department (2002B00002)the Scientific Research Foundation of Hubei Normal University(2003).
文摘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.
基金Supported by the National Natural Science Foundation of China (Tian Yuan Foundation) (No.10426010)the Foundation of Science and Technology of Fujian Province for Young Scholars (2004J0002)the Foundation of Fujian Education Bureau (JA04156, JA0301
文摘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.
基金Supported by the National Natural Science Foundation of China(No.10371034)the Hunan Provincial Natural Science Foundation of China(05JJ40009).
文摘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).
基金supported by the National Natural Science Foundation of China under the Grant(10426010)the Foundation of Science and Technology of Fujian Province for Young Scholars(2004J0002)+3 种基金the Foundation of Fujian Education Bureau(JA04156)the National Natural Science Foundation of China under Grant 60373067the Natural Science Foundation of Jiangsu Province,China under Grants BK2003053Qing-Lan Engineering Project of Jiangsu Province,the Foundation of Southeast University,Nanjing,China under Grant XJ030714
文摘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.
基金Supported by the National Natural Science Foundation of China(No.10171044)the Natural Science Foundation of Jiangsu Province(No.BK2001024)the Foundation for University Key Teachers of the Ministry of Education of China
文摘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.
基金National Natural Science Foundation of China (Grant No.10071022)Mathematical Tianyuan Foudation of China (Grant No.TY10026002-01-05-03) & Shanghai Priority Academic Research.
文摘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 <SUB>1</SUB> and r <SUB>2</SUB> are continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞) with are positive continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous ω-periodic function in R <SUB>+</SUB> = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.
基金This work is supported by the Foundation of Science and Technology of Fujian Province for Young Scholars (2004J0002)the Foundation of Fujian Education Bureau (JA04156).
文摘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.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10271044)
文摘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.
文摘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.
文摘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.
文摘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.
基金This work was supported by the NNSF of China (10071016) the Doctor Program Foundation of the Ministry of Education of China (20010532002) the Key Project of Chinese Ministry of Education (No.[2002]78).
文摘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.
基金Supported by the National Natural Science Foundation of China (No. 10971173)the Scientific Research Foundation of Hunan Provincial Educational Department (No. 05A057)+1 种基金supported by the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Provincethe Construct Program of the Key Discipline in Hunan Province
文摘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.
基金Supported by the National Natural Sciences Foundation of China (No.10171010) Key Project on Sciences and Technology of the Ministry of Education of China (No. Key 01061)the Natural Sciences Foundation for Young Scholar of Northeast Normal Unive
文摘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.
基金This work is supported by the Foundation of Ability Person of Fuzhou University under the grant 0030824228.
文摘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.
基金the Foundation of Education Department of Fujian Province (JAO5204)the Foundation of Science and Technology Department of Fujian Province (2005K027)
文摘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.