Kulakov M.P., Kurilova E.V., Frisman E.Ya.
Synchronization and Bursting Activity in the Model for Two Predator-Prey Systems Coupled By Predator Migration
Mathematical Biology & Bioinformatics. 2019;14(2):588-611.
doi: 10.17537/2019.14.588.
References
- Frisman Y.Y., Kulakov M.P., Revutskaya O.L., Zhdanova O.L., Neverova G.P. The key approaches and review of current researches on dynamics of structured and interacting populations. Computer Research and Modeling. 2019;11(1):119-151 (in Russ.). doi: 10.20537/2076-7633-2019-11-1-119-151
- Mukhopadhyay B., Bhattacharyya R. Role of predator switching in an eco-epidemiological model with disease in the prey. Ecological Modelling. 2009;220(7):931-939. doi: 10.1016/j.ecolmodel.2009.01.016
- Saifuddin Md., Biswas S., Samanta S., Sarkar S., Chattopadhyay J. Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator. Chaos, Solitons & Fractals. 2016;91:270-285. doi: 10.1016/j.chaos.2016.06.009
- Comins H.N., Hassell M.P., May R.M. The spatial dynamics of host-parasitoid systems. J. Animal Ecology. 1992;61:735-748. doi: 10.2307/5627
- Govorukhin V.N., Morgulis A.B., Tyutyunov Yu.V. Slow taxis in a predator-prey model. Doklady Mathematics. 2000;61(3):420-422..
- Tyutyunov Yu.V., Titova L.I., Senina I.N. Prey-taxis destabilizes homogeneous stationary state in spatial Gause-Kolmogorov-type model for predator-prey system. Ecological Complexity. 2017;31:170-180. doi: 10.1016/j.ecocom.2017.07.001
- Krivan V., Eisner J. The effect of the Holling type II functional response on apparent competition. Theoretical Population Biology. 2006;70:421-430.
- Shen Y. Hou Z., Xin H. Transition to burst synchronization in coupled neuron networks. Physical Review E. 2008;77(031920):1-5. doi: 10.1103/PhysRevE.77.031920
- Bakhanova Y.V., Kazakov A.O., Korotkov A.G. Spiral chaos in Lotka-Volterra like models. Middle Volga Mathematical Society Journal. 2017;19(2):13-24 (in Russ.).
- Bakhanova Y.V., Kazakov A.O., Korotkov A.G., Levanova T.A., Osipov G.V. Spiral attractors as the root of a new type of "bursting activity" in the Rosenzweig-MacArthur model. Eur. Phys. J. Special. 2018;227:959-970. doi: 10.1140/epjst/e2018-800025-6
- Huang T., Zhang H. Bifurcation, chaos and pattern formation in a space-and time-discrete predator-prey system. Chaos, Solitons & Fractals. 2016;91:92-107. doi: 10.1016/j.chaos.2016.05.009
- Izhikevich E.M. Neural excitability, spiking and bursting. International Journal of Bifurcation and Chaos. 2000;10(06):1171-1266. doi: 10.1142/S0218127400000840
- Izhikevich E.M. Synchronization of Elliptic Bursters. SIAM REVIEW. 2001;43(2):315-344. doi: 10.1137/S0036144500382064
- Shilnikov A. Cymbalyuk G. Homoclinic bifurcations of periodic orbits en a route from tonic-spiking to bursting in neuron models. Regular and Chaotic Dynamics. 2004;9(3):281-297. doi: 10.1070/RD2004v009n03ABEH000281
- Belykh V.N., Belykh I.V., Colding-J{orgensen M., Mosekilde E. Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models. Eur. Phys. J. E. 2000(3):205-219. doi: 10.1007/s101890070012
- Kolomiets M.L., Shilnikov A.L. Qualitative methods for case study of the Hindmarch–Rose model. Rus. J. Nonlin. Dyn. 2010;6(1):23-52 (in Russ.). doi: 10.20537/nd1001003
- Jansen V.A.A. The Dynamics of Two Diffusively Coupled Predator-Prey Populations. Theoretical Population Biology. 2001;59(2):119-131. doi: 10.1006/tpbi.2000.1506
- Liu Y. The Dynamical Behavior of a Two Patch Predator-Prey Model. Theses, Dissertations, & Master Projects, 2010. 46 p.
- Saha S., Bairagi N., Dana S.K. Chimera states in ecological network under weighted mean-field dispersal of species. Front. Appl. Math. Stat. 2019;5(15):1-11. doi: 10.3389/fams.2019.00015
- Bazykin A.D.Matematicheskaia biofizika vzaimodeistvuiushchikh populiatsii (Mathematical biophysics of interacting populations). Moscow: Nauka; 1985. 181 p. (in Russ.).
- Bazykin A.D. Nonlinear Dynamics of Interacting Populations. Eds. A.I. Khibnik and B. Krauskopf. World Scientific Publishing Co. Pte. Ltd, 1998. 216 p. doi: 10.1142/2284
- Rinaldi S., Muratori S. Slow-fast limit cycles in predator-prey models. Ecological Modelling. 1992;61:287-308. doi: 10.1016/0304-3800(92)90023-8
- Kulakov M. P., Kurilova E. V., Frisman E. Ya. Effects of synchronization by fluctuations in numbers of two predator-prey communities at saturation predator growth and limitation of the victim number. Information Science and Control Systems. 2015;45(3):24-34 (in Russ.).
- Holling C.S. Some characteristics of simple types of predation and parasitism. Canadian Entomologist. 1959;91:385-398. doi: 10.4039/Ent91385-7
- Ghosh S., Bhattacharyya S. A two-patch prey-predator model with food-gathering activity. J. Appl. Math. Comput. 2011;37:497-521. doi: 10.1007/s12190-010-0446-z
- Kang Y. Sasmal S.K., Messan K. A two-patch prey-predator model with predator dispersal driven by the predation strength. Mathematical Biosciences and Engineering. 2017;14(4):843-880. doi: 10.3934/mbe.2017046
- Kurilova E.V., Kulakov M.P. Regional’nye problemy (Regional Problems). 2019;22(1):12-19 (in Russ.). doi: 10.31433/2618-9593-2019-22-1-12-19
- Asada T., Yoshida H. Coefficient criterion for four-dimensional Hopf bifurcations: a complete mathematical characterization and applications to economic dynamics. Chaos, Solitons and Fractals. 2003;18:525-536. doi: 10.1016/S0960-0779(02)00674-4
- Dhooge A., Govaerts W., Kuznetsov Yu.A., Meijer H.G.E., Sautois B. New features of the software MatCont for bifurcation analysis of dynamical systems. Mathematical and Computer Modelling of Dynamical Systems. 2008;14(2):147-175. doi: 10.1080/13873950701742754
- Benoit E., Callot J.L., Diener F., Diener M. Chasse au canard. Collectanea Mathematica. 1981;31-32:37-119.
- Ersoz E.K., Desroches M., Mirasso C.R., Rodrigues S. Anticipation via canards in excitable systems. Chaos. 2019;013111(29). doi: 10.1063/1.5050018
- Fenichel N. Geometric Singular Perturbation Theory for Ordinary Differential Equations. Journal of Differential Equations. 1979;31:53-98. doi: 10.1016/0022-0396(79)90152-9
- Desrochesy M., Kirk V. Spike-Adding in a Canonical Three-Time-Scale Model: Superslow Explosion and Folded-Saddle Canards. SIAM J. Applied dynamical systems. 2018;17(3):1989-2017. doi: 10.1137/17M1143411
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