scholarly journals Asymptotic Behavior of Discrete Time Fuzzy Single Species Model

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Qianhong Zhang ◽  
Fubiao Lin ◽  
Xiaoying Zhong
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solution ◽  
Discrete Time ◽  
Single Species ◽  
Qualitative Behavior ◽  
Initial Value ◽  
Fuzzy Environment ◽  
Surrounding Environment ◽  
Number Of Individuals ◽  
Single Species Model

This work is concerned with the qualitative behavior of discrete time single species model with fuzzy environment xn+1=xnexp⁡A-Bxn,  n=0,1,2,…, where xn denotes the number of individuals of generation n, A is the intrinsic growth rate, and B is interpreted as the carrying capacity of the surrounding environment. xn is a sequence of positive fuzzy number. A,B and the initial value x0 are positive fuzzy numbers. Applying difference of Hukuhara (H-difference), the existence, uniqueness of the positive solution, and global asymptotic behavior of all positive solution with the model are obtained. Moreover a numerical example is presented to show the effectiveness of theoretic results obtained.

ASYMPTOTIC BEHAVIOR OF A TIME-DEPENDENT SINGLE-SPECIES MODEL

Analysis ◽  
1989 ◽  
Vol 9 (3) ◽  
Author(s):  
H.I. Freedman ◽  
V. Sree Hari Rao ◽  
J.W.-H. So
Keyword(s):  
Asymptotic Behavior ◽  
Single Species ◽  
Time Dependent ◽  
Single Species Model

scholarly journals On the sub–diffusion fractional initial value problem with time variable order

2021 ◽  
Vol 10 (1) ◽  
pp. 1301-1315
Author(s):  
Eduardo Cuesta ◽  
Mokhtar Kirane ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Regularity Result ◽  
Time Variable ◽  
Variable Order ◽  
Initial Value ◽  
Integration By Parts ◽  
Integration By Parts Formula ◽  
Variable Order Fractional Derivative

Abstract We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

scholarly journals New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 934
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Kamsing Nonlaopon ◽  
Hijaz Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Discrete Equation ◽  
Qualitative Behavior ◽  
Differential Systems ◽  
Impulsive Differential Systems

The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included.

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

Temporal patterns in the macrobenthic communities of the Hawkesbury estuary, New South Wales

1987 ◽  
Vol 38 (5) ◽  
pp. 607
Author(s):  
AR Jones
Keyword(s):  
Community Composition ◽  
Temporal Patterns ◽  
Single Species ◽  
Species Number ◽  
Community Patterns ◽  
Low Salinity ◽  
Number Of Species ◽  
South Wales ◽  
Physicochemical Factors ◽  
Number Of Individuals

Temporal patterns in number of species, number of individual animals and community composition of the soft-sediment zoobenthos of the Hawkesbury estuary are described and related to physicochemical factors. Replicate grabs were taken at 3-month intervals over 3 years (1977-1979) from sites located in three zones: the lower, middle and upper reaches. The number of species and number of individuals showed significant seasonal and annual differences in all zones. However, the pattern of these differences varied among sites and seasonal differences were not repeatable over years. Similarly, differences in community composition as revealed by classification were not seasonal. In the middle and lower reaches, these differences were apparently caused by the over- riding influence of non-seasonal climatic events, i.e. a major flood in 1978 and a drought throughout 1979. In the first two sampling following the flood, sample values for the numbers of both species and individuals were usually lowest and community composition was distinct from pre-flood and drought times. During the drought, the number of species was usually high and community composition relatively distinct. Whereas the number of species and community composition groupings were both significantly related to river discharge, the number of individuals was significantly correlated with temperature. All community variables were sometimes significantly related to salinity. The identity of numerically dominant species, as determined by Fager rankings, varied among times in both the lower and middle reaches. However, the polychaete Nephtys australiensis and the bivalve mollusc Notospisula trigonella were highest ranked overall in both zones. Community patterns in the low-salinity upper reaches differed from those further downstream by showing little change in numbers of species and community composition following the flood. Only the number of species was significantly correlated with any of the measured physicochemical variables, this being partly due to an influx of species during the drought. Furthermore, the upstream community was always dominated by the polychaete Ceratonereis limnetica and was thus the only community that could be characterised by a single species.

scholarly journals Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yu-Zhu Wang
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Hyperbolic Equation ◽  
Contraction Mapping ◽  
Dimensional Space ◽  
Contraction Mapping Principle ◽  
Nonlinear Hyperbolic Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
The Cauchy Problem

We consider the Cauchy problem for the damped nonlinear hyperbolic equation inn-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle.

Intervention Time in Target-Oriented Chaos Control

2021 ◽  
Vol 31 (09) ◽  
pp. 2150134
Author(s):  
Juan Segura
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Single Species ◽  
Positive Equilibrium ◽  
Population Stability ◽  
Determine Parameter ◽  
And Control ◽  
Parameter Values ◽  
Proportional Feedback

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here we study a discrete-time equation that generalizes the Seno equation by considering the management and exploitation of populations through the target-oriented chaos control method. We investigate the combined effect of timing, targeting, and control on population stability, focusing on global stability. We prove that high enough control values create a positive equilibrium that attracts all positive solutions. We also prove that it is possible to determine parameter values to stabilize the controlled populations at any preset population size. Finally, we investigate the parameter combinations for which the management and exploitation are optimized in different scenarios.

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