zbMATH — the first resource for mathematics

Chaotic dynamic analysis of aquatic phytoplankton system. (English) Zbl 1407.34059
Summary: This study analyzed the effect of nonlinear dynamic parameter of phytoplankton toxin emission on the system. Many previous studies have indicated that the zooplankton, mollusks, and habitat factors generate nonlinear chaotic dynamic behavior, which is hardly controlled random behavior. Therefore, in order to understand in what parameter conditions the system has this nonlinear behavior, the linear and nonlinear behaviors resulting from different conditions are discussed. This study used numerical analysis of differential transformation method to analyze the phase of system and applied bifurcation diagrams, trajectory diagrams, Poincaré maps, and spectrograms to discuss and validate whether the system has chaos phenomenon.

34C28 Complex behavior and chaotic systems of ordinary differential equations
92D25 Population dynamics (general)
92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
Full Text: DOI
[1] Chattopadhayay, J.; Sarkar, R. R.; Mandal, S., Toxin-producing plankton may act as a biological control for planktonic blooms—field study and mathematical modelling, Journal of Theoretical Biology, 215, 3, 333-344, (2002)
[2] Chattopadhyay, J.; Sarkar, R. R., Chaos to order: preliminary experiments with a population dynamics models of three trophic levels, Ecological Modelling, 163, 1-2, 45-50, (2003)
[3] Gakkhar, S.; Singh, A., A delay model for viral infection in toxin producing phytoplankton and zooplankton system, Communications in Nonlinear Science and Numerical Simulation, 15, 11, 3607-3620, (2010) · Zbl 1222.37098
[4] Dixon, P. A.; Milicich, M. J.; Sugihara, G., Episodic fluctuations in larval supply, Science, 283, 5407, 1528-1530, (1999)
[5] Erbe, L. H.; Freedman, H. I.; Sree Hari Rao, V., Three-species food-chain models with mutual interference and time delays, Mathematical Biosciences, 80, 1, 57-80, (1986) · Zbl 0592.92024
[6] Rai, V.; Upadhyay, R. K., Evolving to the edge of chaos: chance or necessity?, Chaos, Solitons and Fractals, 30, 5, 1074-1087, (2006) · Zbl 1142.92344
[7] Hansen, F. C., Trophic interactions between zooplankton and Phaeocystis cf. globosa, Helgoländer Meeresuntersuchungen, 49, 1–4, 283-293, (1995)
[8] Kaitala, V.; Ylikarjula, J.; Heino, M., Non-unique population dynamics: basic patterns, Ecological Modelling, 135, 2-3, 127-134, (2000)
[9] Rai, V.; Upadhyay, R. K., Chaotic population dynamics and biology of the top-predator, Chaos, Solitons & Fractals, 21, 5, 1195-1204, (2004) · Zbl 1057.92056
[10] Turchin, P.; Ellner, S. P., Living on the edge of chaos: Population dynamics of fennoscandian voles, Ecology, 81, 11, 3099-3116, (2000)
[11] Upadhyay, R. K., Multiple attractors and crisis route to chaos in a model food-chain, Chaos, Solitons & Fractals, 16, 5, 737-747, (2003) · Zbl 1033.92038
[12] Upadhyay, R. K.; Chattopadhyay, J., Chaos to order: role of toxin producing phytoplankton in aquatic systems, Nonlinear Analysis: Modelling and Control, 10, 4, 383-396, (2005) · Zbl 1147.92327
[13] Wang, C.; Jang, M.; Yeh, Y., Bifurcation and nonlinear dynamic analysis of a flexible rotor supported by relative short gas journal bearings, Chaos, Solitons and Fractals, 32, 2, 566-582, (2007)
[14] Wang, C., Theoretical and nonlinear behavior analysis of a flexible rotor supported by a relative short herringbone-grooved gas journal-bearing system, Physica D: Nonlinear Phenomena, 237, 18, 2282-2295, (2008) · Zbl 1142.70328
[15] Wang, C., Application of a hybrid method to the nonlinear dynamic analysis of a flexible rotor supported by a spherical gas-lubricated bearing system, Nonlinear Analysis, Theory, Methods and Applications, 70, 5, 2035-2053, (2009) · Zbl 1180.76017
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.