Spatiotemporal dynamics of a predator-prey system with linear harvesting rate

Mathematical Problems in Engineering

Volumn 2014, Issue , 2014, Pages

  Baek, Hunki ^a  

^a Catholic University of Daegu   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DISCRETE FOURIER TRANSFORMS; HOPF BIFURCATION; NUMERICAL MODELS; PREDATOR PREY SYSTEMS;

HARVESTING SYSTEM; PREDATOR - PREY SYSTEM; SPATIAL FREQUENCY; SPATIAL PATTERN FORMATION; SPATIALLY EXTENDED SYSTEMS; SPATIO-TEMPORAL DYNAMICS; TURING BIFURCATION; TWO DIMENSIONAL SPACES;

ECOSYSTEMS;

EID: 84899904048     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2014/625973     Document Type: Article

References (31)

1. Arditi R., Ginzburg L. R., Coupling in predator-prey dynamics: ratio-dependence. Journal of Theoretical Biology 1989 139 3 311 326 2-s2.0-4944258042
2. Gakkhar S., Naji R. K., Chaos in seasonally perturbed ratio-dependent prey-predator system. Chaos, Solitons and Fractals 2003 15 1 107 118 10.1016/S0960-0779(02)00114-5 MR1925583 ZBL1033.92026 (Pubitemid 34991812)
3. Kuang Y., Beretta E., Global qualitative analysis of a ratio-dependent predator-prey system. Journal of Mathematical Biology 1998 36 4 389 406 10.1007/s002850050105 MR1624192 ZBL0895.92032 (Pubitemid 128735354)
4. Wang Q., Fan M., Wang K., Dynamics of a class of nonautonomous semi-ratio-dependent predator-prey systems with functional responses. Journal of Mathematical Analysis and Applications 2003 278 2 443 471 10.1016/S0022- 247X(02)00718-7 MR1974018 ZBL1029.34042 (Pubitemid 36530148)
5. Cosner C., Deangelis D. L., Ault J. S., Olson D. B., Effects of spatial grouping on the functional response of predators. Theoretical Population Biology 1999 56 1 65 75 2-s2.0-0033180314 10.1006/tpbi.1999.1414 (Pubitemid 29395865)
6. Gutierrez A. P., Physiological basis of ratio-dependent predator-prey theory: the metabolic pool model as a paradigm. Ecology 1992 73 5 1552 1563 2-s2.0-0027084787 (Pubitemid 23397217)
7. Xiao D., Jennings L. S., Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting. SIAM Journal on Applied Mathematics 2005 65 3 737 753 10.1137/S0036139903428719 MR2136029 ZBL1094.34024 (Pubitemid 40892123)
8. Xiao D., Li W., Han M., Dynamics in a ratio-dependent predator-prey model with predator harvesting. Journal of Mathematical Analysis and Applications 2006 324 1 14 29 10.1016/j.jmaa.2005.11.048 MR2262452 ZBL1122.34035 (Pubitemid 44426297)
9. Camara B. I., Aziz-Alaoui M. A., Turing and Hopf patterns formation in a predator-prey model with Leslie-Gower-type functional response. Dynamics of Continuous, Discrete & Impulsive Systems B. Applications & Algorithms 2009 16 4 479 488 MR2547538 ZBL1173.35340
10. Banerjee M., Self-replication of spatial patterns in a ratio-dependent predator-prey model. Mathematical and Computer Modelling 2010 51 1-2 44 52 10.1016/j.mcm.2009.07.015 MR2571157 ZBL1190.37085
11. Liu R., Liaw S., Oscillatory turing patterns in a simple reaction-diffusion system. Journal of the Korean Physical Society 2007 50 1 I 234 238 2-s2.0-33846703716
12. Upadhyay R. K., Wang W., Thakur N. K., Spatiotemporal dynamics in a spatial plankton system. Mathematical Modelling of Natural Phenomena 2010 5 5 102 122 10.1051/mmnp/20105507 MR2681230 ZBL1197.92049
13. Wang W., Liu Q., Jin Z., Spatiotemporal complexity of a ratio-dependent predator-prey system. Physical Review E-Statistical, Nonlinear, and Soft Matter Physics 2007 75 5 9 2-s2.0-34347224051 10.1103/PhysRevE.75.051913 051913 (Pubitemid 47000968)
14. Yang L., Dolnik M., Zhabotinsky A. M., Epstein I. R., Pattern formation arising from interactions between turing and wave instabilities. Journal of Chemical Physics 2002 117 15 7259 7265 2-s2.0-0037109593 10.1063/1.1507110 (Pubitemid 35354171)
15. Zhang L., Wang W., Xue Y., Spatiotemporal complexity of a predator-prey system with constant harvest rate. Chaos, Solitons & Fractals 2009 41 1 38 46 10.1016/j.chaos.2007.11.009 MR2533319 ZBL1198.35127
16. Ji L., Wu C., Qualitative analysis of a predator-prey model with constant-rate prey harvesting incorporating a constant prey refuge. Nonlinear Analysis: Real World Applications 2010 11 4 2285 2295 10.1016/j.nonrwa.2009.07. 003 MR2661899 ZBL1203.34070
17. Xia J., Liu Z., Yuan R., Ruan S., The effects of harvesting and time delay on predator-prey systems with Holling type II functional response. SIAM Journal on Applied Mathematics 2009 70 4 1178 1200 10.1137/080728512 MR2546358 ZBL1203.34137
18. Xiao D., Ruan S., Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting. Fields Institute Communications 1999 21 493 509
19. Pal S., Chatterjee S., Das K. P., Chattopadhyay J., Role of competition in phytoplankton population for the occurrence and control of plankton bloom in the presence of environmental fluctuations. Ecological Modelling 2009 220 2 96 110 2-s2.0-56949089956 10.1016/j.ecolmodel.2008.10.001
20. Xiao M., Cao J., Hopf bifurcation and non-hyperbolic equilibrium in a ratio-dependent predator-prey model with linear harvesting rate: analysis and computation. Mathematical and Computer Modelling 2009 50 3-4 360 379 10.1016/j.mcm.2009.04.018 MR2542783 ZBL1185.34047
21. Alonso D., Bartumeus F., Catalan J., Mutual interference between predators can give rise to turing spatial patterns. Ecology 2002 83 1 28 34 2-s2.0-0036141801 (Pubitemid 34067676)
22. Berenstein I., Dolnik M., Yang L., Zhabotinsky A. M., Epstein I. R., Turing pattern formation in a two-layer system: superposition and superlattice patterns. Physical Review E-Statistical, Nonlinear, and Soft Matter Physics 2004 70 4 2-s2.0-41349109750 10.1103/PhysRevE.70.046219 046219 (Pubitemid 40010353)
23. Guin L. N., Haque M., Mandal P. K., The spatial patterns through diffusion-driven instability in a predator-prey model. Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems 2012 36 5 1825 1842 10.1016/j.apm.2011.05.055 MR2878150 ZBL1242.35207
24. Guin L. N., Existence of spatial patterns in a predator-prey model with self- and cross-diffusion. Applied Mathematics and Computation 2014 226 320 335 10.1016/j.amc.2013.10.005 MR3144313
25. Liao X., Chen Y., Zhou S., Traveling wavefronts of a prey-predator diffusion system with stage-structure and harvesting. Journal of Computational and Applied Mathematics 2011 235 8 2560 2568 10.1016/j.cam.2010.11.008 MR2763167 ZBL1207.92047
26. Sun G.-Q., Jin Z., Zhao Y.-G., Liu Q.-X., Li L., Spatial pattern in a predator-prey system with both self- and cross-diffusion. International Journal of Modern Physics C. Computational Physics 2009 20 1 71 84 10.1142/ S0129183109013467 MR2494327 ZBL1155.35476
27. Turing A. M., The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London 1952 237 641 37 72
28. Medvinsky A. B., Petrovskii S. V., Tikhonova I. A., Malchow H., Li B.-L., Spatiotemporal complexity of plankton and fish dynamics. SIAM Review 2002 44 3 311 370 10.1137/S0036144502404442 MR1951363 ZBL1001.92050
29. Kozlova I., Singh M., Easton A., Ridland P., Twospotted spider mite predator-prey model. Mathematical and Computer Modelling 2005 42 11-12 1287 1298 10.1016/j.mcm.2005.01.036 MR2185351 (Pubitemid 41774469)
30. Prum R. O., Torres R. H., A fourier tool for the analysis of coherent light scattering by bio-optical nanostructures. Integrative and Comparative Biology 2003 43 4 591 610 2-s2.0-1542752201
31. Fasani S., Rinaldi S., Factors promoting or inhibiting Turing instability in spatially extended prey-predator systems. Ecological Modelling 2011 222 18 3449 3452 2-s2.0-80052936667 10.1016/j.ecolmodel.2011.07.002