|
[1]
|
Reigada, R., et al. (2003) Plankton Blooms Induced by Turbulent Flows. Proceedings of the Royal Society B: Biological Sciences, 270, 875-880. [Google Scholar] [CrossRef] [PubMed]
|
|
[2]
|
Truscott, J.E. and Brindley, J. (1994) Ocean Plankton Populations as Excitable Media. Bulletin of Mathematical Biology, 56, 981-998. [Google Scholar] [CrossRef]
|
|
[3]
|
Luo, J.H. (2013) Phytoplankton-Zooplankton Dynamics in Periodic Environments Taking into Account Eutrophication. Mathematical Biosciences, 245, 126-136. [Google Scholar] [CrossRef] [PubMed]
|
|
[4]
|
Almeida Machado, P. (1978) Dinoflagellate Blooms on the Bra-zilian South Atlantic Coast. In: Toxic Dinoflagellate Blooms, Elsevier, Amsterdam, The Netherlands, 29.
|
|
[5]
|
Jef, H., et al. (2018) Cyanobacterial Blooms. Nature Reviews Microbiology, 16, 471-483. [Google Scholar] [CrossRef] [PubMed]
|
|
[6]
|
Miller, D.A. (1997) Turning Back the Harmful Red Tide. Nature, 388, 513-514. [Google Scholar] [CrossRef]
|
|
[7]
|
Smith, H.V. (1983) Low Nitrogen to Phosphorus Ratios Favor Dominance by Blue-Green Algae in Lake Phytoplankton. Science, 221, 669-671. [Google Scholar] [CrossRef] [PubMed]
|
|
[8]
|
Ryther, J.H. and Dunstan, W.M. (1971) Nitrogen, Phosphorus, and Eutrophication in the Coastal Marine Environment. Science, 171, 1008-1013. [Google Scholar] [CrossRef] [PubMed]
|
|
[9]
|
Bertalanffy, L.V. and Woodger, J.H. (1935) Modern Theories of Development.
|
|
[10]
|
Yu, H.G., Zhao, M. and Agarwal, R.P. (2014) Stability and Dynamics Analysis of Time Delayed Eutrophication Ecological Model Based upon the Zeya Reservoir. Mathematics and Computers in Simulation, 97, 53-67. [Google Scholar] [CrossRef]
|
|
[11]
|
Wu, D., Zhang, H., Cao, J., et al. (2013) Stability and Bifur-cation Analysis of a Nonlinear Discrete Logistic Model with Delay. Discrete Dynamics in Nature and Society, 2013, 1-7. [Google Scholar] [CrossRef]
|
|
[12]
|
Tian, Y.L. and Weng, P.X. (2011) Stability Analysis of Diffusive Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes. Acta Applicandae Mathematicae, 114, 173-192. [Google Scholar] [CrossRef]
|
|
[13]
|
Yue, Z.M. and Wang, W.J. (2013) Qualitative Analysis of a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth. Discrete Dynamics in Nature and Society, 2013, Article ID: 267173. [Google Scholar] [CrossRef]
|
|
[14]
|
Tang, S.Y., Tang, B., Wang, A.L., et al. (2015) Holling II Predator-Prey Impulsive Semi-Dynamic Model with Complex Poincare Map. Nonlinear Dynamics, 87, 1575-1596. [Google Scholar] [CrossRef]
|
|
[15]
|
Fu, J.B. and Chen, L.S. (2012) Study of a Semi-Ratio Preda-tor-Prey Model with Impulsive Control. Journal of Beihua University (Natural Science), 13, 621-626.
|
|
[16]
|
Hu, S.C., Lakshmikantham, V. and Leela, S. (1989) Impusive Differential Systems and the Pulse Phenomena. The Journal of Mathematical Analysis and Applications, 137, 605-612. [Google Scholar] [CrossRef]
|
|
[17]
|
Bainov, D.D. and Simeonov, P.S. (1993) Impulsive Differ-ential Equations: Periodic Solutions and Applications. Longman Scientific and Technical, New York.
|
|
[18]
|
Bainov, D. and Covachev, V. (1994) Impulsive Differential Equations with a Small Parameter. [Google Scholar] [CrossRef]
|
|
[19]
|
Bainov, D.D. and Simeonov, P.S. (1993) Impulsive Differential Equations: Asymptotic Properties of the Solutions. World Scientific, Singapore.
|
|
[20]
|
Lakshmikantham, V. (1989) Theory of Impulsive Differential Equations. World Scientific, Singapore. [Google Scholar] [CrossRef]
|
|
[21]
|
Samoilenko, A.M. (1995) Impulsive Differential Equations. World Scientific, Singapore. [Google Scholar] [CrossRef]
|
|
[22]
|
Dai, C.J., Zhao, M. and Chen, L.S. (2012) Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control. Journal of Applied Mathematics, 2012, Article ID: 534276. [Google Scholar] [CrossRef]
|
|
[23]
|
Dai, C.J. and Zhao, M. (2012) Mathematical and Dynamic Analysis of a Prey-Predator Model in the Presence of Alternative Prey with Impulsive State Feedback Control. Discrete Dynamics in Nature and Society, 2012, Article ID: 724014. [Google Scholar] [CrossRef]
|
|
[24]
|
Dai, C.J., Zhao, M. and Chen, L.S. (2012) Homoclinic Bifurcation in Semi-Continuous Dynamic Systems. International Journal of Bio-mathematics, 5, 1-19. [Google Scholar] [CrossRef]
|
|
[25]
|
Nie, L.F., et al. (2009) Existence and Stability of Periodic Solution of a Predator-Prey Model with State-Dependent Impulsive Effects. Mathematics and Computers in Simulation , 79, 2122-2134. [Google Scholar] [CrossRef]
|
|
[26]
|
Tang, S.Y. and Chen, L.S. (2002) Density-Dependent Birth Rate, Birth Pulses and Their Population Dynamic Consequences. Journal of Mathematical Biology, 44, 185-199. [Google Scholar] [CrossRef] [PubMed]
|
|
[27]
|
Ballinger, G. and Liu, X. (1997) Permanence of Population Growth Models with Impulsive Effects. Mathematical and Computer Modelling, 26, 59-72. [Google Scholar] [CrossRef]
|
|
[28]
|
Zhang, S.W. (2001) The Study for One-compartment Model of Peridic Pulse Dosage. Journal of Anshan Teachers College, 3, 19-22.
|
|
[29]
|
Xiao, Q.Z., et al. (2015) Dynamics of an Impulsive Predator-Prey Logistic Population Model with State-Dependent. Elsevier Science Inc., New York, 220-230. [Google Scholar] [CrossRef]
|
|
[30]
|
Zhang, T.Q., Ma, W.B., et al. (2015) Periodic Solution of a Prey-Predator Model with Nonlinear State Feedback Control. Applied Mathematics and Computation, 266, 95-107. [Google Scholar] [CrossRef]
|
|
[31]
|
Wei, C.J. and Chen, L.S. (2012) A Leslie-Gower Pest Management Model with Impulsive State Feedback Control. Journal of Biomathematics, 27, 621-628.
|
|
[32]
|
Guo, H.J., Chen, L.S. and Song, X.Y. (2015) Qualitative Analysis of Impulsive State Feedback Control to an Algae-Fish System with Bistable Property. Applied Mathematics and Computation, 271, 905-922. [Google Scholar] [CrossRef]
|
|
[33]
|
Huppert, A., Blasius, B. and Stone, L. (2002) A Model of Phyto-plankton Blooms. The American Naturalist, 159, 156-171. [Google Scholar] [CrossRef] [PubMed]
|
|
[34]
|
Chakraborty, S., Tiwari, P.K., Misra, A.K. and Chattopadhyay, J. (2015) Spatial Dynamics of a Nutrient-Phytoplankton System with Toxic Effect on Phytoplankton. Mathematical Biosciences, 264, 94-100. [Google Scholar] [CrossRef] [PubMed]
|
|
[35]
|
Wang, B.B., Zhao, M., Dai, C.J., Yu, H., et al. (2016) Dynamics Analysis of a Nutrient-Phytoplankton Model with Time Delays. Discrete Dynamics in Nature and Society, 2016, Article ID: 9797624. [Google Scholar] [CrossRef]
|
|
[36]
|
Wang, Y.P., Zhao, M., Pan, X.H. and Dai, C.J. (2014) Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control. Discrete Dynamics in Nature and Society, 2014, Article ID: 914647. [Google Scholar] [CrossRef]
|
|
[37]
|
Deng, Y.L., Zhao, M., Yu, H.G., et al. (2015) Dynamical Analysis of a Nitrogen-Phosphorus-Phytoplankton Model. Discrete Dynamics in Nature and Society, 2015, 1-8. [Google Scholar] [CrossRef]
|
|
[38]
|
Dai, C.J., Zhao, M., Yu, H., et al. (2015) Delay-Induced Instability in a Nutrient-Phytoplankton System with Flow. Physical Review E, 91, Article ID: 032929. [Google Scholar] [CrossRef]
|
|
[39]
|
Dai, C.J., Zhao, M., Yu, H., et al. (2019) Dynamics Induced by Delay in a Nutrient -Phytoplankton Model with Multiple Delays. Complexity, 2019, Article ID: 3879626. [Google Scholar] [CrossRef]
|
|
[40]
|
Chen, L.S. (2013) Theory and Application of Semi-Continuous Dy-namical System. Journal of Yulin Normal University (Natural Science), 34, 1-10.
|
|
[41]
|
Chen, L.S. (2011) Pest Control and Geometric Theory of Semi-Continuous Dynamical System. Journal of Beihua University (Natural Science), 2, 1-9.
|
|
[42]
|
Liang, Z.Q., et al. (2016) Qualitative Analysis of a Predator-Prey System with Mutual Interference and Im-pulsive State Feedback Control. Nonlinear Dynamics, 87, 1-15. [Google Scholar] [CrossRef]
|