scholarly journals Permanence in a Discrete Mutualism Model with Infinite Deviating Arguments and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Changjin Xu ◽  
Yusen Wu
Keyword(s):  
Sufficient Conditions ◽  
Feedback Controls ◽  
Difference Inequality ◽  
Deviating Arguments ◽  
Inequality Theory ◽  
The Difference ◽  
Mutualism Model

We propose and deal with a discrete mutualism model with infinite deviating arguments and feedback controls. Sufficient conditions which guarantee the permanence of the system are obtained by using the difference inequality theory. The paper ends with brief conclusions.

scholarly journals Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

2017 ◽  
Vol 15 (1) ◽  
pp. 218-232
Author(s):  
Lin Lu ◽  
Yi Lian ◽  
Chaoling Li
Keyword(s):  
Sufficient Conditions ◽  
Suitable Condition ◽  
Multiple Delays ◽  
Stable Periodic Solution ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Inequality Theory ◽  
Stable Periodic ◽  
Cooperation Model ◽  
The Difference

Abstract This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.

scholarly journals Global Attractivity in a Discrete Mutualism Model with Infinite Deviating Arguments

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Xiangdong Xie ◽  
Yalong Xue ◽  
Runxin Wu
Keyword(s):  
Global Attractivity ◽  
Sufficient Conditions ◽  
Deviating Arguments ◽  
Mutualism Model

A set of sufficient conditions is obtained for the global attractivity of the following two-species discrete mutualism model with infinite deviating arguments: x1(k+1)=x1kexp⁡r1(K1+α1∑s=0+∞J2sx2k-s)/(1+∑s=0+∞J2sx2k-s)-x1k and  x2(k+1)=x2kexp⁡r2(K2+α2∑s=0+∞J1sx1k-s)/(1+∑s=0+∞J1sx1k-s)-x2k, where ri,Ki,αi, i=1,2, are all positive constants, ∑j=1+∞Ji(n)=1, and αi>Ki. Our results generalize the main result of Yang et al. (2014).

scholarly journals Dynamic Behavior of Positive Solutions for a Leslie Predator-Prey System with Mutual Interference and Feedback Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Cong Zhang ◽  
Nan-jing Huang ◽  
Chuan-xian Deng
Keyword(s):  
Global Attractivity ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Mutual Interference ◽  
Periodic Case ◽  
Feedback Controls ◽  
Predator Prey ◽  
Prey System ◽  
Inequality Theory ◽  
Nonautonomous Case

We consider a Leslie predator-prey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee the existence, uniqueness, and stability of a positive periodic solution.

Permanence and extinction of stochastic regime-switching mutualism model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050028
Author(s):  
Guangying Lv ◽  
Beibei Zhang
Keyword(s):  
Regime Switching ◽  
Diffusion Processes ◽  
Sufficient Conditions ◽  
Switching Diffusion ◽  
Random Switching ◽  
The Difference ◽  
Mutualism Model

This paper is concerned with the permanence and extinction of a stochastic regime-switching mutualism model. We aim to find the difference between the stochastic mutualism model with regime-switching and without regime-switching. By studying ergodicity of regime-switching diffusion processes, we establish the sufficient conditions to estimate the permanence and extinction of a species in a random switching environment. Moreover, compared with the system without switching, the advantages of the stochastic regime-switching mutualism model are given.

scholarly journals Feedback Control Variables Have No Influence on the Permanence of a Discreten-Species Schoener Competition System with Time Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Qianqian Su ◽  
Na Zhang
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Time Delays ◽  
Feedback Controls ◽  
Control Variables ◽  
Difference Inequality ◽  
Competition System ◽  
Inequality Theory

We consider a discreten-species Schoener competition system with time delays and feedback controls. By using difference inequality theory, a set of conditions which guarantee the permanence of system is obtained. The results indicate that feedback control variables have no influence on the persistent property of the system. Numerical simulations show the feasibility of our results.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

1997 ◽  
Vol 4 (6) ◽  
pp. 557-566
Author(s):  
B. Půža
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Vector Function ◽  
Unique Solvability ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Deviating Arguments ◽  
Measurable Functions

Abstract Sufficient conditions of solvability and unique solvability of the boundary value problem u (m)(t) = f(t, u(τ 11(t)), . . . , u(τ 1k (t)), . . . , u (m–1)(τ m1(t)), . . . . . . , u (m–1)(τ mk (t))), u(t) = 0, for t ∉ [a, b], u (i–1)(a) = 0 (i = 1, . . . , m – 1), u (m–1)(b) = 0, are established, where τ ij : [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn → Rn is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

A Direct Rotatability Criterion for Spherical Four-Bar Linkages

1995 ◽  
Vol 117 (4) ◽  
pp. 597-600 ◽  
Author(s):  
K. C. Gupta ◽  
R. Ma
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Absolute Value ◽  
The Difference ◽  
Necessary And Sufficient ◽  
Four Bar Linkage

The necessary and sufficient conditions for the full input rotatability in a spherical four-bar linkage are proved. The direct criterion is: for all twist angles α in the range [0, π], the excess (deficit) of the sum of the frame and input twist angles over (from) π should, in absolute value, be greater than that for the coupler and follower twist angles; the difference between the follower and input twist angles, in absolute value, should be greater than that for the coupler and follower twist angles. Application of the direct criterion to full rotatability of other links are discussed and some variations in the form of the criterion are developed.

A Direct Rotatability Criterion for Spherical Four-Bar Linkages

1994 ◽  
Author(s):  
R. Ma ◽  
K. C. Gupta
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Absolute Value ◽  
The Difference ◽  
Necessary And Sufficient ◽  
Four Bar Linkage

Abstract The necessary and sufficient conditions for the full input rotatability in a spherical four bar linkage are proved. The direct criterion is: for all twist angles α in the range [0, π], the excess (deficit) of the sum of the frame and input twist angles over (from) π should, in absolute value, be greater than that for the coupler and follower twist angles; the difference between the follower and input twist angles, in absolute value, should be greater than that for the coupler and follower twist angles. Application of the direct criterion to full rotatability of other links are discussed and some variations in the form of the criterion are developed.

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