Pattern Formation in Tri-Trophic Ratio-Dependent Food Chain Model

作者: Dawit Melese , Sunita Gakkhar

DOI: 10.4236/AM.2011.212213

关键词: CombinatoricsNeumann boundary conditionReaction–diffusion systemBifurcationTrophic levelSpatial ecologyBiological systemMathematicsPattern formationFood chainHopf bifurcation

摘要: In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient the emergence of patterns obtained. The results numerical simulations reveal formation labyrinth coexistence spotted stripe-like patterns.

参考文章(23)
Weiming Wang, Lei Zhang, Yakui Xue, Zhen Jin, Spatiotemporal pattern formation of Beddington-DeAngelis-type predator-prey model arXiv: Populations and Evolution. ,(2008)
Weiming Wang, Quan-Xing Liu, Zhen Jin, Spatiotemporal complexity of a ratio-dependent predator-prey system Physical Review E. ,vol. 75, pp. 051913- ,(2007) , 10.1103/PHYSREVE.75.051913
Alexander B. Medvinsky, Sergei V. Petrovskii, Irene A. Tikhonova, Horst Malchow, Bai-Lian Li, Spatiotemporal Complexity of Plankton and Fish Dynamics SIAM Review. ,vol. 44, pp. 311- 370 ,(2002) , 10.1137/S0036144502404442
Alan Mathison Turing, The Chemical Basis of Morphogenesis Philosophical Transactions of the Royal Society B. ,vol. 237, pp. 37- 72 ,(1952) , 10.1098/RSTB.1952.0012
Sergei Petrovskii, Bai-Lian Li, Horst Malchow, Transition to spatiotemporal chaos can resolve the paradox of enrichment Ecological Complexity. ,vol. 1, pp. 37- 47 ,(2004) , 10.1016/J.ECOCOM.2003.10.001
Wonlyul Ko, Inkyung Ahn, Analysis of ratio-dependent food chain model Journal of Mathematical Analysis and Applications. ,vol. 335, pp. 498- 523 ,(2007) , 10.1016/J.JMAA.2007.01.089
S.-H. Lee, H.K. Pak, H.S. Wi, T.-S. Chon, T. Matsumoto, Growth dynamics of domain pattern in a three-trophic population model Physica A-statistical Mechanics and Its Applications. ,vol. 334, pp. 233- 242 ,(2004) , 10.1016/J.PHYSA.2003.11.017
Malay Banerjee, Sergei Petrovskii, Self-organised spatial patterns and chaos in a ratio-dependent predator-prey system Theoretical Ecology. ,vol. 4, pp. 37- 53 ,(2011) , 10.1007/S12080-010-0073-1
Horst Malchow, Birgit Radtke, Malaak Kallache, Alexander B Medvinsky, Dmitry A Tikhonov, Sergei V Petrovskii, None, Spatio-temporal pattern formation in coupled models of plankton dynamics and fish school motion Nonlinear Analysis-real World Applications. ,vol. 1, pp. 53- 67 ,(2000) , 10.1016/S0362-546X(99)00393-4