scholarly journals Dynamic Behaviors in a Droop Model for Phytoplankton Growth in a Chemostat with Nutrient Periodically Pulsed Input

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Kai Wang ◽  
Zhidong Teng ◽  
Xueliang Zhang
Keyword(s):  
Periodic Solution ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Phytoplankton Growth ◽  
Dynamic Behaviors ◽  
Droop Model ◽  
New Criteria

The dynamic behaviors in a droop model for phytoplankton growth in a chemostat with nutrient periodically pulsed input are studied. A series of new criteria on the boundedness, permanence, extinction, existence of positive periodic solution, and global attractivity for the model are established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.

scholarly journals Global attractivity of positive periodic solution to periodic Lotka–Volterra competition systems with pure delay

2006 ◽  
Vol 228 (2) ◽  
pp. 580-610 ◽  
Author(s):  
Xianhua Tang ◽  
Daomin Cao ◽  
Xingfu Zou
Keyword(s):  
Periodic Solution ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Pure Delay

EXISTENCE AND GLOBAL ATTRACTIVITY OF A POSITIVE PERIODIC SOLUTION FOR A NON-AUTONOMOUS PREDATOR-PREY MODEL UNDER VIRAL INFECTION

2009 ◽  
Vol 02 (04) ◽  
pp. 419-442 ◽  
Author(s):  
FENGYAN ZHOU
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Positive Periodic Solution ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

A new non-autonomous predator-prey system with the effect of viruses on the prey is investigated. By using the method of coincidence degree, some sufficient conditions are obtained for the existence of a positive periodic solution. Moreover, with the help of an appropriately chosen Lyapunov function, the global attractivity of the positive periodic solution is discussed. In the end, a numerical simulation is used to illustrate the feasibility of our results.

scholarly journals Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Yunhui Zeng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Positive Periodic Solution ◽  
Multiple Delays ◽  
Neutral Delay ◽  
Mawhin’S Continuation Theorem ◽  
Volterra Models ◽  
Functional Differential ◽  
New Criteria

By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory fork-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse:x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))],  t≠tk,  k∈Z+;  x(tk+)=x(tk-)+θk(x(tk)),  k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

Existence and global attractivity of positive periodic solution to a Lotka–Volterra model

2010 ◽  
Vol 11 (5) ◽  
pp. 4054-4061 ◽  
Author(s):  
Xiaoli Wang ◽  
Zengji Du ◽  
Jing Liang
Keyword(s):  
Periodic Solution ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Volterra Model
Sign in / Sign up

Export Citation Format

Share Document