Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/patterned-solutions-of-a-homogenous-diffusive-predator-prey-system-of-5q3Rbi0TDQ
References (23)
-
A. Medvinsky, S. Petrovskii, I. Tikhonova, H. Malchow, Bai-lian Li (2002)
Spatiotemporal Complexity of Plankton and Fish DynamicsSIAM Rev., 44
-
N. Kazarinoff, P. Driessche (1978)
A model predator-prey system with functional responseBellman Prize in Mathematical Biosciences, 39
-
Fengqi Yi, Junjie Wei, Junping Shi (2009)
Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion systemAppl. Math. Lett., 22
-
Michael Ward, Juncheng Wei (2003)
Hopf bifurcation of spike solutions for the shadow Gierer–Meinhardt modelEuropean Journal of Applied Mathematics, 14
-
Jianxing Liu, Fengqi Yi, Junjie Wei (2010)
Multiple bifurcation Analysis and Spatiotemporal Patterns in a 1-d Gierer-Meinhardt Model of MorphogenesisInt. J. Bifurc. Chaos, 20
-
N. Kazarinov, P. Driessche (1978)
A model predator-prey systems with functional response.Math. Biosci., 39
-
R. May (2019)
Stability and Complexity in Model Ecosystems, 6
-
T. Schoener (1974)
STABILITY AND COMPLEXITY IN MODEL ECOSYSTEMSEvolution, 28
-
S. Liaw, C. Yang, Ruey-Tarng Liu, J. Hong (2001)
Turing model for the patterns of lady beetles.Physical review. E, Statistical, nonlinear, and soft matter physics, 64 4 Pt 1
-
Fengqi Yi, Junjie Wei, Junping Shi (2009)
Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩Journal of Differential Equations, 246
-
Puchen Liu, Fengqi Yi, Qiang Guo, Jun Yang, Wei Wu (2008)
Analysis on global exponential robust stability of reaction–diffusion neural networks with S-type distributed delaysPhysica D: Nonlinear Phenomena, 237
-
A. Turing (1952)
The chemical basis of morphogenesisBulletin of Mathematical Biology, 52
-
A. Wijeratne, Fengqi Yi, Junjie Wei (2009)
Bifurcation analysis in the diffusive Lotka–Volterra system: An application to market economyChaos Solitons & Fractals, 40
-
Fengqi Yi, Junjie Wei, Junping Shi (2008)
Diffusion-driven instability and bifurcation in the Lengyel-Epstein systemNonlinear Analysis-real World Applications, 9
-
Lii-Perng Liou, Kuo‐shung Cheng (1988)
Global stability of a predator-prey systemJournal of Mathematical Biology, 26
-
M. Ward, Juncheng Wei (2003)
Hopf Bifurcations and Oscillatory Instabilities of Spike Solutions for the One-Dimensional Gierer-Meinhardt ModelJournal of Nonlinear Science, 13
-
Rui Peng, Junping Shi (2009)
Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction caseJournal of Differential Equations, 247
-
A. Turing (1952)
The chemical basis of morphogenesis.Philos. Trans. Roy. Soc. London B., 237
-
Wonlyul Ko, Kimun Ryu (2006)
Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refugeJournal of Differential Equations, 231
-
F. Menalled, Richard Smith (2009)
Plant-Provided Food for Carnivorous Insects: a Protective Mutualism and Its Applications, 35
-
Zhifen Zhang (1986)
Proof of the uniqueness theorem of limit cycles of generalized liénard equationsApplicable Analysis, 23
-
P. Turchin (2003)
Complex population dynamics: a theoretical/empirical synthesis -
H. Freedman (1982)
Deterministic mathematical models in population ecologyBiometrics, 38
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-016-0628-z
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, a diffusive predator-prey system of Holling type functional III is considered. For one hand, we considered the possibility of the occurrence of Turing patterns of the system. Our results show that there is no Turing patterns found in the system. On the other hand, we performed detailed Hopf bifurcation analysis to the systems, and showed that the system have multiple oscillatory patterns. Moreover, we also derived the conditions to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions. Computer simulations are included to support our theoretical analysis.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Oct 1, 2016