scholarly journals Extinction and stationary distribution of a competition system with distributed delays and higher order coupled noises

2020 ◽  
Vol 17 (4) ◽  
pp. 3240-3251
Author(s):  
Jing Hu ◽  
◽  
Zhijun Liu ◽  
Lianwen Wang ◽  
Ronghua Tan
Keyword(s):  
Stationary Distribution ◽  
Higher Order ◽  
Distributed Delays ◽  
Competition System

POSITIVE PERIODIC SOLUTIONS FOR A GENERALIZED IMPULSIVE N-SPECIES GILPIN–AYALA COMPETITION SYSTEM WITH CONTINUOUSLY DISTRIBUTED DELAYS ON TIME SCALES

2011 ◽  
Vol 04 (01) ◽  
pp. 23-34 ◽  
Author(s):  
TIANWEI ZHANG ◽  
YONGKUN LI
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Competition System ◽  
Periodic Environment

In this paper, we study a generalized impulsive n-species Gilpin–Ayala competition system with continuously distributed delays on time scales in periodic environment, which is more general and more realistic than the classical Lotka–Volterra competition system. By using a fixed point theorem of strict-set-contraction, some sufficient conditions are obtained for the existence of at least one positive periodic solution. Finally, we present an example to illustrate that our results are effective.

Dynamical behavior of a stochastic multigroup staged-progression HIV model with saturated incidence rate and higher-order perturbations

2021 ◽  
pp. 2150051
Author(s):  
Qun Liu ◽  
Daqing Jiang
Keyword(s):  
Incidence Rate ◽  
Stationary Distribution ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Hiv Model ◽  
Progression Model ◽  
Saturated Incidence Rate ◽  
Biological Interpretation ◽  
Saturated Incidence

In this paper, we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HIV with saturated incidence rate. We obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a suitable stochastic Lyapunov function. In addition, we make up adequate conditions for complete eradication and wiping out the infectious disease. In a biological interpretation, the existence of a stationary distribution implies that the disease will prevail and persist in the long term. Finally, examples and numerical simulations are introduced to validate our theoretical results.

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