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STABILITY AND BIFURCATION ANALYSIS OF A LOTKA-VOLTERRA MODEL WITH TIME DELAYS
Xu, Changjin,Liao, Maoxin The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.1
In this paper, a Lotka-Volterra model with time delays is considered. A set of sufficient conditions for the existence of Hopf bifurcation are obtained via analyzing the associated characteristic transcendental equation. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form method and center manifold theory. Finally, the main results are illustrated by some numerical simulations.
PERMANENCE OF A TWO SPECIES DELAYED COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTING
XU, CHANGJIN,ZU, YUSEN Korean Mathematical Society 2015 대한수학회보 Vol.52 No.4
In this paper, a two species competitive model with stage structure and harvesting is investigated. By using the differential inequality theory, some new sufficient conditions which ensure the permanence of the system are established. Our result supplements the main results of Song and Chen [Global asymptotic stability of a two species competitive system with stage structure and harvesting, Commun. Nonlinear Sci. Numer. Simul. 19 (2001), 81-87].
Bifurcation analysis of a delayed predator-prey model of prey migration and predator switching
Changjin Xu,Xianhua Tang,Maoxin Liao 대한수학회 2013 대한수학회보 Vol.50 No.2
In this paper, a class of delayed predator-prey models of prey migration and predator switching is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.
PERMANENCE OF A TWO SPECIES DELAYED COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTING
Changjin Xu,Yusen Zu 대한수학회 2015 대한수학회보 Vol.52 No.4
In this paper, a two species competitive model with stage structure and harvesting is investigated. By using the differential inequality theory, some new sufficient conditions which ensure the permanence of the system are established. Our result supplements the main results of Song and Chen [Global asymptotic stability of a two species competitive system with stage structure and harvesting, Commun. Nonlinear Sci. Numer. Simul. 19 (2001), 81–87].
Changjin Xu,Peiluan Li 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.2
This paper deals with a class of memristor-based bidirectional associative memory (BAM) neural networks with leakage delays and time-varying delays. With the aid of the framework of Filippov solutions, Chain rule and some inequality techniques, a sufficient condition which ensures the boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks with leakage delays and time-varying delays is established. Applying a new approach involving Yoshizawa-like theorem, we prove the existence of periodic solution of the memristor-based BAM neural networks. By using the theory of set-valued maps and functional differential inclusions, Lyapunov functional, a set of sufficient conditions which guarantee the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks are derived. An example is given to illustrate the applicability and effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known studies of Li et al. [Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural networks 75 (2016) 97-109.]
BIFURCATION ANALYSIS OF A DELAYED EPIDEMIC MODEL WITH DIFFUSION
Xu, Changjin,Liao, Maoxin Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.2
In this paper, a class of delayed epidemic model with diffusion is investigated. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation are also carried out to support our analytical findings. Finally, biological explanations and main conclusions are given.
Stability and bifurcation analysis of a Lotka-Volterra model with time delays
Changjin Xu,Maoxin Liao 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.1
In this paper, a Lotka-Volterra model with time delays is considered. A set of sufficient conditions for the existence of Hopf bifurcation are obtained via analyzing the associated characteristic transcendental equation. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form method and center manifold theory. Finally, the main results are illustrated by some numerical simulations.
BIFURCATION ANALYSIS OF A DELAYED PREDATOR-PREY MODEL OF PREY MIGRATION AND PREDATOR SWITCHING
Xu, Changjin,Tang, Xianhua,Liao, Maoxin Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
In this paper, a class of delayed predator-prey models of prey migration and predator switching is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.
On p-th Moment Exponential Stability for Stochastic Cellular Neural Networks with Distributed Delays
Changjin Xu,Lilin Chen,Peiluan Li 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.3
In this paper, a class of stochastic cellular neural networks with distributed delays are investigated. With the help of the method of variation parameter and inequality techniques, some sufficient conditions for the p-th moment exponential stability of the system are established. An example is given to illustrate the feasibility and effectiveness of our main results. Our results obtained in this paper improve and generalize some earlier works reported in the literature.
Xu, Hongtao,Wu, Changjin,Xiahou, Zhao,Jung, Ranju,Li, Ying,Liu, Chunli Springer US 2017 Nanoscale research letters Vol.12 No.1
<P>Five percent of Fe-doped ZnO (ZnO:Fe) thin films were deposited on Pt/TiO<SUB>2</SUB>/SiO<SUB>2</SUB>/Si substrates by a spin-coating method. The films were annealed without (ZnO:Fe-0T) and with a pulsed magnetic field of 4 T (ZnO:Fe-4TP) to investigate the magnetic annealing effect on the resistance switching (RS) behavior of the Pt/ZnO:Fe/Pt structures. Compared with the ZnO:Fe-0T film, the ZnO:Fe-4TP film showed improved RS performance regarding the stability of the set voltage and the resistance of the high resistance state. Transmission electron microscopy and X-ray photoelectron spectroscopy analyses revealed that the ZnO:Fe-4TP film contains more uniform grains and a higher density of oxygen vacancies, which promote the easier formation of conducting filaments along similar paths and the stability of switching parameters. These results suggest that external magnetic fields can be used to prepare magnetic oxide thin films with improved resistance switching performance for memory device applications.</P>