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Page 6834 of Mathematical Reviews Vol. , Issue 2001I
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2001
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In spite of the apparent simplicity of Volterra-Lotka models, these are still mathematically challenging, particularly those with time delays and, even more, those with time delays and diffusion. ...
., 2, Gordon and Breach, Amsterdam, 2000. This paper is devoted to the study of a Volterra-Lotka competition model with diffusion and time delays. ...
Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays
2021
Symmetry
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In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. ...
Steady-state curves and Hopf bifurcation maps were created and discussed in detail. ...
Acknowledgments: The author thanks the anonymous reviewers for their helpful comments and suggestions. ...
doi:10.3390/sym13112217
fatcat:ihvi6mj74jbqrhc5q7gakkyhy4
Page 5286 of Mathematical Reviews Vol. , Issue 97H
[page]
1997
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The paper deals with a system of delay differential equations with a single delay, derived from a PDE model with diffu- sion and intraspecific competition, originally proposed by N. F. ...
competitive Lotka-Volterra systems made by May and Leonard. ...
Page 228 of Mathematical Reviews Vol. , Issue 2002A
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2002
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The dynamics of the two systems (with and without diffusion) in the neighborhood of E, are related by taking the delay t > 0 as a parameter
It is proven that a Hopf bifurcation occurs in (1) as the delay ...
Ed. 21 (2001), no. 1, 94-101
“In this paper the existence of positive periodic solu- tions of a class of periodic Lotka-Volterra type systems with delays is studied. ...
Page 4346 of Mathematical Reviews Vol. , Issue 2001F
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2001
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Yamanobe and H. Fukai, A mathematical aspect of neural coding (229-238); Jifang Sun and Guibin Hou, Bifurcation of periodic solutions in Lotka-Volterra systems with finite delay (239- 245); Y. ...
Cheng, A genetic study on the ef- fects of opaque-2 and polygenes on kernel quality traits in maize (143-147); Gangwen Lu and Zhengyi Lu, Global stability for n-species Lotka-Volterra systems with delay ...
A note on Hopf bifurcations in a delayed diffusive Lotka–Volterra predator–prey system
2011
Computers and Mathematics with Applications
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The diffusive Lotka-Volterra predator-prey system with two delays is reconsidered here. ...
We also obtain that in a special case, a Hopf bifurcation of spatial inhomogeneous periodic solutions occurs in the system. ...
In the last 15 years especially, the stability/instability and bifurcation of equilibrium solutions for reaction-diffusion equations/systems with a delay effect have been considered extensively. ...
doi:10.1016/j.camwa.2011.07.011
fatcat:usamnermnjgcdoq76dn4haj2be
Page 2911 of Mathematical Reviews Vol. , Issue 93e
[page]
1993
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In this paper the authors consider a prey-predator system with dif- fusion, and discuss the combined effect of the diffusion and the inherent death rate of the predator on the stability of the equilib- ...
The authors use Lyapunov’s direct method to find stability con- ditions and domains of attraction for perturbed Lotka-Volterra systems of the form x = ax —bxy+D(y-—x), py=cy—dxy+ D(x -—y), where a,b,c ...
Page 3802 of Mathematical Reviews Vol. , Issue 2000e
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2000
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A general Lotka-Volterra system of one predator and two prey is investigated with regard to reachable periodic solutions. ...
Summary: “In this paper, the general n-species nonautonomous competitive Lotka-Volterra systems are studied. ...
Page 7101 of Mathematical Reviews Vol. , Issue 95k
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1995
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These systems model the population dynamics of one species with diffusion, delay, and feedback control. ...
Summary: “A stochastic system containing two prey species and a predator species and having Lotka-Volterra type of interactions is considered. ...
Page 8760 of Mathematical Reviews Vol. , Issue 2004k
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2004
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The authors consider a neutral Lotka-Volterra system with peri- odic coefficients and delays. ...
There is a confusion in the pa- per: the authors claim that this is the first work to study a neutral Lotka-Volterra system with unbounded delays; however, the re- quirements that the delays are continuous ...
Review of trends in theory and practice of nonlinear differential equations, lecture notes in pure and applied mathematics
1986
Computers and Mathematics with Applications
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descent methods, reaction-diffusion equations, Lyapunov stability, stochastic differential equations, comparison and frequency domain techniques, delay differential equations, method of upper and lower ...
equations, generalized Hopf bifurcation and exchange of stability and nonlinear elliptic problems. ...
descent methods, reaction-diffusion equations, Lyapunov stability, stochastic differential equations, comparison and frequency domain techniques, delay differential equations, method of upper and lower ...
doi:10.1016/0898-1221(86)90186-0
fatcat:dwlcprpb7nhn3dlp7mohlk6u6a
The diffusive Lotka–Volterra predator–prey system with delay
2015
Mathematical Biosciences
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Semi-analytical solutions for the diffusive Lotka-Volterra predator-prey system with delay are considered in one and two-dimensional domains. ...
Semi-analytical solutions for the diffusive Lotka-Volterra predator-prey system with delay are considered in one and two-dimensional domains. ...
Al Noufaey gratefully thanks Taif University in Saudi Arabia for awarding him a PhD scholarship to study at the University of Wollongong, Australia. ...
doi:10.1016/j.mbs.2015.09.010
pmid:26471317
fatcat:qeudanoy3fe55jvpfm46m2tvhq
Page 4405 of Mathematical Reviews Vol. , Issue 95g
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1995
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Summary: “The stability of the fixed-points of general predator- prey models with Volterra-type distributed delays in the inter- species interaction terms is considered. ...
Here we discuss the stability behaviour of this model.”
95g:92023 92D40 35K57 92D25
Zheng, Si Ning (PRC-DUT-AM; Dalian)
A reaction-diffusion system of a prey with three genotypes and a predator. ...
Page 4711 of Mathematical Reviews Vol. , Issue 85j
[page]
1985
Mathematical Reviews
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The author considers Lotka- Volterra systems with diffusion. ...
Kishimoto, Kazuo 85j:92021 The diffusive Lotka- Volterra system with three species can have a stable nonconstant equilibrium solution.
J. Math. Biol. 16 (1982/83), no. 1, 103-112. ...
Page 4681 of Mathematical Reviews Vol. , Issue 92h
[page]
1992
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Stable and unstable regions on the parametric plane are separated.”
92h:92014 92D25 35K40 47H15
Voller, R. L. (D-DSLD)
Solving Volterra-Lotka systems with diffusion by monotone iteration.
J. Math. ...
, Jian Quan
Stability of a class of population growth models with gap-distributed delay. ...
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