Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic model with Markovian switching and Lévy noise

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5869-5883
Author(s):  
Sheng Wang ◽  
Linshan Wang ◽  
Tengda Wei
Keyword(s):  
Logistic Model ◽  
Necessary Conditions ◽  
Sample Path ◽  
Analytical Techniques ◽  
Markovian Switching ◽  
Matrix Analysis ◽  
Stationary Probability Distribution ◽  
Stochastic Permanence ◽  
Sufficient And Necessary Conditions ◽  
Stochastic Logistic Model

In this paper, stochastic permanence and extinction of a stochastic logistic model with Markovian switching and L?vy noise are investigated by combining stochastic analytical techniques with M-matrix analysis. Sufficient and necessary conditions of stochastic permanence and extinction are obtained. In the case of stochastic permanence, both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the logistic model. Finally, our conclusions are illustrated through an example.

scholarly journals Permanence and Extinction of a Stochastic Delay Logistic Model with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chun Lu ◽  
Xiaohua Ding
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Population Model ◽  
Logistic Model ◽  
Necessary Conditions ◽  
Biological Significance ◽  
Jump Process ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Sufficient And Necessary Conditions

This paper is concerned with a stochastic delay logistic model with jumps. Sufficient and necessary conditions for extinction are obtained as well as stochastic permanence. Numerical simulations are introduced to support the theoretical analysis results. The results show that the jump process can affect the properties of the population model significantly, which conforms to biological significance.

TWO PATCHES IMPULSIVE DIFFUSION PERIODIC SINGLE-SPECIES LOGISTIC MODEL

2010 ◽  
Vol 03 (01) ◽  
pp. 127-141 ◽  
Author(s):  
ZIJIAN LIU ◽  
ZHIDONG TENG ◽  
LONG ZHANG
Keyword(s):  
Periodic Solution ◽  
Iterative Method ◽  
Numerical Simulations ◽  
Logistic Model ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Impulsive Diffusion ◽  
Sufficient And Necessary Conditions

In this paper, we study a periodic single-species logistic system with impulsive diffusion in two patches. By using the iterative method, sufficient and necessary conditions on the existence, uniqueness and global attractivity of positive periodic solution and the extinction of species for this system are established. Two examples and numerical simulations are presented to illustrate the feasibility of our results.

scholarly journals Dynamics Analysis of a Stochastic Hybrid Logistic Model with Delay and Two-Pulse Perturbations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Haokun Qi ◽  
Hua Guo
Keyword(s):  
Growth Rate ◽  
Logistic Model ◽  
Dynamics Analysis ◽  
Stochastic Disturbances ◽  
Stochastic Permanence ◽  
Lower Upper ◽  
Persistence In The Mean ◽  
Stochastic Logistic Model ◽  
The Mean ◽  
Impulsive Harvesting

In this paper, we propose and discuss a stochastic logistic model with delay, Markovian switching, Lévy jump, and two-pulse perturbations. First, sufficient criteria for extinction, nonpersistence in the mean, weak persistence, persistence in the mean, and stochastic permanence of the solution are gained. Then, we investigate the lower (upper) growth rate of the solutions. At last, we make use of Matlab to illustrate the main results and give an explanation of biological implications: the large stochastic disturbances are disadvantageous for the persistence of the population; excessive impulsive harvesting or toxin input can lead to extinction of the population.

scholarly journals Dynamical Behavior of a Stochastic Delayed One-Predator and Two-Mutualistic-Prey Model with Markovian Switching and Different Functional Responses

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Rensheng He ◽  
Zuoliang Xiong ◽  
Desheng Hong
Keyword(s):  
Lyapunov Functions ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Matrix Analysis ◽  
Stationary Probability ◽  
Functional Responses ◽  
Stationary Probability Distribution ◽  
Stochastic Permanence ◽  
Prey Model ◽  
Telegraph Noise

We propose a stochastic delayed one-predator and two-mutualistic-prey model perturbed by white noise and telegraph noise. By theM-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established, respectively. These conditions are all dependent on the subsystems’ parameters and the stationary probability distribution of the Markov chain. We also investigate another asymptotic property and finally give two examples and numerical simulations to illustrate main results.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

Perfect colorings of patterns with multiple orbits

2019 ◽  
Vol 75 (6) ◽  
pp. 814-826
Author(s):  
Allan Junio ◽  
Ma. Lailani Walo
Keyword(s):  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

This paper studies colorings of patterns with multiple orbits, particularly those colorings where the orbits share colors. The main problem is determining when such colorings become perfect. This problem is attacked by characterizing all perfect colorings of patterns through the construction of sufficient and necessary conditions for a coloring to be perfect. These results are then applied on symmetrical objects to construct both perfect and non-perfect colorings.

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