scholarly journals Periodic solutions for complex-valued neural networks of neutral type by combining graph theory with coincidence degree theory

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Zhengqiu Zhang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Graph Theory ◽  
Periodic Solutions ◽  
Neutral Type ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Complex Valued

scholarly journals Existence and stability of periodic solutions for a class of generalized nonautonomous neural networks with distributed delays

2005 ◽  
Vol 2005 (7) ◽  
pp. 997-1005
Author(s):  
Yongkun Li ◽  
Lifei Zhu ◽  
Wenxiang Liu
Keyword(s):  
Neural Networks ◽  
Global Stability ◽  
Periodic Solutions ◽  
Lyapunov Functions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Distributed Delays ◽  
Coincidence Degree Theory ◽  
Existence And Stability

By using the continuation theorem of coincidence degree theory and Lyapunov functions, we study the existence and global stability of periodic solutions for a class of generalized nonautonomous neural networks with distributed delays.

scholarly journals Multiple Periodic Solutions of a Nonautonomous Plant-Hare Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongfei Gao ◽  
P. J. Y. Wong ◽  
Y. H. Xia ◽  
Xiaoqing Yuan
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
New Technique ◽  
Positive Periodic Solutions ◽  
Multiple Periodic Solutions

Based on Mawhin's coincidence degree theory, sufficient conditions are obtained for the existence of at leasttwopositive periodic solutions for a plant-hare model with toxin-determined functional response (nonmonotone). Some new technique is used in this paper, because standard arguments in the literature are not applicable.

scholarly journals 2 N POSITIVE PERIODIC SOLUTIONS TO N SPECIES NON‐AUTONOMOUS LOTKA‐VOLTERRA UNIDIRECTIONAL FOOD CHAINS WITH HARVESTING TERMS

2010 ◽  
Vol 15 (3) ◽  
pp. 313-326 ◽  
Author(s):  
Yongkun Li ◽  
Kaihong Zhao
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Food Chains ◽  
Positive Periodic Solutions ◽  
Mawhin Continuation Theorem

By using the Mawhin continuation theorem of coincidence degree theory and some results on inequalities, we establish the existence of 2 n positive periodic solutions for n species non‐autonomous Lotka‐Volterra unidirectional food chains with harvesting terms. Two examples are given to illustrate the effectiveness of our results.

scholarly journals Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harvesting Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yongzhi Liao ◽  
Yongkun Li ◽  
Xiaoyan Dou
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Predator Prey ◽  
Prey System

By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.

scholarly journals Multiple Periodic Solutions of Generalized Gause-Type Predator-Prey Systems with Nonmonotonic Numerical Responses and Impulse

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Yunhui Zeng
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Multiple Periodic Solutions

We consider an impulsive periodic generalized Gause-type predator-prey model with nonmonotonic numerical responses. Using the continuation theorem of coincidence degree theory, we present an easily verifiable sufficient condition on the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results extend and improve some known criteria.

Existence of Periodic Solutions to a Class of Environmental Mathematical Model

2012 ◽  
Vol 518-523 ◽  
pp. 1540-1543
Author(s):  
Jun Yi Yin
Keyword(s):  
Mathematical Model ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Number Of Species ◽  
Existence Of Periodic Solutions

This paper has studied a class of environmental mathematical model by using the coincidence degree theory, verified the existence of periodic solutions of the system to meet certain conditions, and revealed a relationship between a number of species in the system and pollution.

scholarly journals Periodic solutions of periodic generalized food limited model

2001 ◽  
Vol 25 (4) ◽  
pp. 265-271 ◽  
Author(s):  
Yongkun Li
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Distributed Delays ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
State Dependent

By using the continuation theorem of coincidence degree theory, the existence of positive periodic solutions for a periodic generalized food limited model with state dependent delays and distributed delays is studied, respectively.

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