scholarly journals On a periodic neutral logistic equation

1991 ◽  
Vol 33 (3) ◽  
pp. 281-286 ◽  
Author(s):  
K. Gopalsamy ◽  
Xue-Zhong He ◽  
Lizhi Wen
Keyword(s):  
Periodic Solution ◽  
Positive Integer ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Logistic Equation ◽  
Periodic Functions ◽  
Neutral Delay ◽  
Periodic Delay ◽  
Image Position ◽  
Delay Logistic Equation

The oscillatory and asymptotic behaviour of the positive solutions of the autonomous neutral delay logistic equationwith r, c, T, K ∈ (0, ∞) has been recently investigated in [2]. More recently the dynamics of the periodic delay logistic equationin which r, K are periodic functions of period τ and m is a positive integer is considered in [6]. The purpose of the following analysis is to obtain sufficient conditions for the existence and linear asymptotic stability of a positive periodic solution of a periodic neutral delay logistic equationin which Ṅ denotes and r, K, c are positive continuous periodic functions of period τ at and m is a positive integer. For the origin and biological relevance of (1.3) we refer to [2].

scholarly journals On the dynamics of a periodic delay logistic equation with diffusion

1992 ◽  
Vol 45 (1) ◽  
pp. 113-134
Author(s):  
K. Gopalasamy ◽  
Pei-Xuan Weng
Keyword(s):  
Periodic Solution ◽  
Positive Integer ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Logistic Equation ◽  
Periodic Functions ◽  
Periodic Delay ◽  
Globally Attractive ◽  
Image Position ◽  
Delay Logistic Equation

Sufficient conditions are obtained for the existence of a globally attractive positive periodic solution of the periodic diffusive delay logistic systemin which τ and K are positive periodic functions of period τ, n is a positive integer and ö is a nonnegative number; sufficient conditions are also obtained for all positive solutions to be oscillatory about the periodic solution.

scholarly journals On a periodic mutualism model

2001 ◽  
Vol 42 (4) ◽  
pp. 569-580 ◽  
Author(s):  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Mutualism Model ◽  
Image Position

AbstractSufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the mutualism modelwhere ri, Ki, αi ∈ C(R, R+) and αi > Ki, i = 1, 2, τi, σi ∈ C(R, R+), i = 1, 2, and ri, Ki, αi, τi, σi (i = 1, 2) and functions of period ω > 0.

Global attractivity in the delay logistic equation with variable parameters

1990 ◽  
Vol 107 (3) ◽  
pp. 579-590 ◽  
Author(s):  
B. G. Zhang ◽  
K. Gopalsamy
Keyword(s):  
Asymptotic Stability ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Logistic Equation ◽  
Linear Variation ◽  
Variable Parameters ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Image Position ◽  
Delay Logistic Equation

AbstractUsing a non-linear variation of constants formula, sufficient conditions are derived for the global asymptotic stability of the trivial solution of

Oscillations of Second Order Neutral Differential Equations

1993 ◽  
Vol 36 (4) ◽  
pp. 485-496 ◽  
Author(s):  
Shigui Ruan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractIn this paper, we consider the oscillatory behavior of the second order neutral delay differential equationwhere t ≥ t0,T and σ are positive constants, a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.

Oscillation and Global Attractivity in a Periodic Delay Equation

1996 ◽  
Vol 39 (3) ◽  
pp. 275-283 ◽  
Author(s):  
J. R. Graef ◽  
C. Qian ◽  
P. W. Spikes
Keyword(s):  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
All Solutions ◽  
Periodic Delay ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient

AbstractConsider the delay differential equationwhere α(t) and β(t) are positive, periodic, and continuous functions with period w > 0, and m is a nonnegative integer. We show that this equation has a positive periodic solution x*(t) with period w. We also establish a necessary and sufficient condition for every solution of the equation to oscillate about x*(t) and a sufficient condition for x*(t) to be a global attractor of all solutions of the equation.

scholarly journals An Impulsive Periodic Single-Species Logistic System with Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Chenxue Yang ◽  
Mao Ye ◽  
Zijian Liu
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Patchy Environment ◽  
Estimation Technique ◽  
Numerical Examples ◽  
Integrable Form

We study a single-species periodic logistic type dispersal system in a patchy environment with impulses. On the basis of inequality estimation technique, sufficient conditions of integrable form for the permanence and extinction of the system are obtained. By constructing an appropriate Lyapunov function, conditions for the existence of a unique globally attractively positive periodic solution are also established. Numerical examples are shown to verify the validity of our results and to further discuss the model.

Analysis of nonautonomous two species system in a polluted environment

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
G. Samanta
Keyword(s):  
Periodic Solution ◽  
Population Growth ◽  
Asymptotic Behaviour ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Volterra Model ◽  
Asymptotically Stable ◽  
Polluted Environment ◽  
Globally Asymptotically Stable ◽  
Bounded Functions

AbstractIn this paper, a two-species nonautonomous Lotka-Volterra model of population growth in a polluted environment is proposed. Global asymptotic behaviour of this model by constructing suitable bounded functions has been investigated. It is proved that each population for competition, predation and cooperation systems respectively is uniformly persistent (permanent) under appropriate conditions. Sufficient conditions are derived to confirm that if each of competition, predation and cooperation systems respectively admits a positive periodic solution, then it is globally asymptotically stable.

scholarly journals Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Shengmao Fu ◽  
Fei Qu
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Time Dependent ◽  
Asymptotically Stable ◽  
Positive Periodic Solutions ◽  
Periodic Functions ◽  
Globally Asymptotically Stable ◽  
Periodic Model ◽  
Asymptotically Periodic

The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions(u1T,u2T,u3T),  (u1T,u2T,u3T)such thatuiT≤uiT  (i=1,2,3), and the sector{(u1,u2,u3):uiT≤ui≤uiT,  i=1,2,3}is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable.

Hilbert transforms and almost periodic functions

1960 ◽  
Vol 56 (4) ◽  
pp. 354-366 ◽  
Author(s):  
J. Cossar
Keyword(s):  
Hilbert Transform ◽  
Sufficient Conditions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Hilbert Transforms ◽  
Cauchy Principal ◽  
Principal Value ◽  
Image Position ◽  
The Hilbert Transform

The Hilbert transform, Hf, of a function f is defined by Hf = g, whereP denoting the Cauchy principal value and the integral being assumed to exist in some sense. When f is suitably restricted, Hf exists andIn the first part of Theorem 1 sufficient conditions are given for the validity of (1·2) rather more general than those of Wood ((6), p. 31). The present proof is based on the well-known condition of Riesz for the validity of (1·2), namely, that f is Lp(−∞, ∞) for some p > 1, and on the ‘Parseval’ relation (Lemma 3, (b)), which was used in a similar way by Hardy ((3), p. 110).

On a Theorem of Rav Concerning Egyptian Fractions

1975 ◽  
Vol 18 (1) ◽  
pp. 155-156 ◽  
Author(s):  
William A. Webb
Keyword(s):  
Positive Integer ◽  
Elementary Proof ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Egyptian Fractions ◽  
Image Position ◽  
Complete Bibliography ◽  
Necessary And Sufficient

Problems involving Egyptian fractions (rationals whose numerator is 1 and whose denominator is a positive integer) have been extensively studied. (See [1] for a more complete bibliography). Some of the most interesting questions, many still unsolved, concern the solvability ofwhere k is fixed.In [2] Rav proved necessary and sufficient conditions for the solvabilty of the above equation, as a consequence of some other theorems which are rather complicated in their proofs. In this note we give a short, elementary proof of this theorem, and at the same time generalize it slightly.

Sign in / Sign up

Export Citation Format

Share Document