Exploring dynamical complexity in diffusion driven predator-prey systems: effect of toxin producing phytoplankton and spatial heterogeneities. (English) Zbl 1198.37131
Not reviewed.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
MSC:
| 37N25 | Dynamical systems in biology |
| 92-08 | Computational methods for problems pertaining to biology |
| 92D25 | Population dynamics (general) |
References:
| [1] | Rai, V.; Anand, M.; Upadhyay, R. K., Trophic structure and dynamical complexity in simple ecological models, Ecol Complex, 4, 212-222 (2007) |
| [2] | May, R. M., Simple mathematical models with very complicated dynamics, Nature, 261, 459-467 (1976) · Zbl 1369.37088 |
| [3] | Upadhyay, R. K.; Rai, V., Why chaos is rarely observed in natural populations?, Chaos, Solitons and Fractals, 8, 1933-1939 (1997) |
| [4] | Upadhyay, R. K.; Iyengar, S. R.K.; Rai, V., Chaos: an ecological reality?, Int J Bifur Chaos, 8, 1325-1333 (1998) · Zbl 0935.92037 |
| [5] | Upadhyay, R. K.; Rai, V., Crisis-limited chaotic dynamics in ecological systems, Chaos, Solitons and Fractals, 12, 205-218 (2001) · Zbl 0977.92033 |
| [6] | Rai, V., Chaos in natural populations: edge or wedge?, Ecol Complex, 1, 127-138 (2004) |
| [7] | Rai, V.; Upadhyay, R. K., Evolving to the edge of chaos: chance or necessity?, Chaos, Solitons and Fractals, 30, 1074-1087 (2006) · Zbl 1142.92344 |
| [8] | Xu, R.; Chaplain, M. A.J.; Davidson, F. A., Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays, Chaos, Solitons and Fractals, 30, 974-992 (2006) · Zbl 1142.35477 |
| [9] | Jiang, G.; Lu, Q.; Qian, L., Complex dynamics of a Holling type II prey-predator system with state feedback control, Chaos, Solitons and Fractals, 31, 448-461 (2007) · Zbl 1203.34071 |
| [10] | Li, W. T.; Wu, S. L., Travelling waves in a diffusive predator-prey model with Holling type-III functional response, Chaos, Solitons and Fractals, 37, 476-486 (2008) · Zbl 1155.37046 |
| [11] | Medvinsky, A.; Petrovskii, S. V.; Tikhonova, I.; Malchow, H.; Li, Bai-Lian, Spatiotemporal complexity of plankton and fish dynamics, SIAM Rev, 44, 311-370 (2002) · Zbl 1001.92050 |
| [12] | Malchow, H.; Hilker, F. M.; Petrovskii, S. V., Noise and productivity dependence of spatiotemporal pattern formation in a prey-predator system, Discrete Continuous Dynamical Syst B, 4, 3, 705-711 (2004) · Zbl 1114.92068 |
| [13] | Petrovskii, S. V.; Malchow, H., Wave of chaos: new mechanism of pattern formation in spatiotemporal population dynamics, Theor Popul Biol, 59, 157-174 (2001) · Zbl 1035.92046 |
| [14] | Upadhyay, R. K.; Kumari, N.; Rai, V., Wave of chaos in a diffusive system: generating realistic patterns of patchiness in plankton-fish dynamics, Chaos, Solitons and Fractals, 40, 1, 262-276 (2009) · Zbl 1197.37121 |
| [15] | Engstro¨m, J.; Viherluoto, M.; Viitasalo, M., Effects of toxic and non-toxic cyanobacteria on grazing, zooplanktivory and survival of the mysid shrimp Mysis mixta, J Exp Mar Biol Ecol, 257, 2, 263-280 (2001) |
| [16] | Pohnert, G.; Steinke, M.; Tollrian, R., Chemical cues, defense metabolites and the shaping of pelagic interspecies interactions, Trends Ecol Evol, 22, 198-204 (2007) |
| [17] | Bergkovist, J.; Selander, E.; Pavia, H., Induction of toxin production in dinoflagellates: the grazer makes a difference, Oecologia, 156, 1, 147-154 (2008) |
| [18] | Scheffer, M., Fish and nutrients interplay determines algal biomass: a minimal model, OIKOS, 62, 271-282 (1991) |
| [19] | Malchow, H.; Radtke, B.; Kallache, M.; Medvinsky, A.; Tikhonov, D.; Petrovskii, S., Spatio-temporal pattern formation in coupled models of plankton dynamics and fish school motion, Non linear Anal Real World Appl, 1, 53-67 (2000) · Zbl 0986.92041 |
| [20] | Tikhonova, I.; Li, B.; Malchow, H.; Medvinsky, A., The impact of the phytoplankton growth rule on spatial and temporal dynamics of plankton communities in a heterogeneous environment, Biofizika, 48, 891-899 (2003) |
| [21] | Pascual, M., Diffusion Induced chaos in a spatial predator-prey system, Proc R Soc Lond B, 251, 1-7 (1993) |
| [22] | Rai, V.; Jayaraman, G., Is diffusion induced chaos robust?, Curr Sci, 84, 7, 925-929 (2003) |
| [23] | Rosenzweig, M. L.; MacArthur, R. H., Graphical representations and stability conditions of predator-prey interactions, Am Nat, 97, 209-223 (1963) |
| [24] | Jang, M. H.; Kyong, H.; Joo, G. J.; Takamura, N., Toxin production of cyanobacteria is increased by exposure to zooplankton, Freshwater Biol, 48, 1540-1550 (2003) |
| [25] | Hu, H.; Shi, Y.; Cong, W., Improvement in growth and toxin production of Alexandrium tamarense by two-step culture method, J Appl Phycol, 18, 119-126 (2006) |
| [26] | Donk, E. V.; Hessen, D. O., Grazing resistance in nutrient-stressed phytoplankton, Oecologia, 93, 508-511 (1993) |
| [27] | Turner, J. T.; Tester, P. A., Toxic marine phytoplankton, zooplankton grazers and pelagic food webs, Limnol Oceanogr, 42, 1203-1214 (1997) |
| [28] | Okubo, A., Diffusion and ecological problems: mathematical models (1980), Springer: Springer Berlin · Zbl 0422.92025 |
| [29] | Ludwig, D.; Jones, D.; Holling, C., Qualitative analysis of an insect outbreak system: the spruce budworm and forest, J Anim Ecol, 47, 315-332 (1978) |
| [30] | Kirk, K.; Gilbert, J., Variations in herbivore response to chemical defences: zooplankton foraging on toxic cyanobacteria, Ecology, 73, 2208 (1992) |
| [31] | Nielsen, T. G.; Kiorboe, T.; Bjornsen, P. K., Effects of Chrysocromulina polylepis sub surface bloom on the plankton community, Mar Ecol Prog Ser, 62, 21-35 (1990) |
| [32] | Turchin, P.; Ellner, S. P., Living on the edge of chaos: population dynamics of Fennoscandian voles, Ecology, 81, 3099-3116 (2000) |
| [33] | Rai, V.; Upadhyay, R. K., Chaotic population dynamics and biology of the top-predator, Chaos, Solitons and Fractals, 21, 1195-1204 (2004) · Zbl 1057.92056 |
| [34] | Sarkar, R. R.; Chattopadhyay, J., Occurrence of planktonic blooms under environmental fluctuations and its possible control mechanism-mathematical models and experimental observations, J Theor Biol, 224, 501-516 (2003) · Zbl 1465.92098 |
| [35] | Nejstgaard J, C.; Solberg P, T., Repression of copepod feeding and fecundity by the toxichaptophyte Prymnesium patelliferum, Sarsia, 81, 339-344 (1996) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
