Liliya S. Ibragimova, Marat G. Yumagulov, Airat R. Ishbirdin, Majya M. Ishmuratova
Mathematical Modeling of Dynamics of the Number of Specimens in a Biological Population Under Changing External Conditions on the Example of the Burzyan Wild-Hive Honeybee (Apismellifera L., 1758)
Mathematical Biology & Bioinformatics. 2017;12(1):224-236.
doi: 10.17537/2017.12.224.
References
- Bratus A.S., Novozhilov A.S., Platonov A.P. Dinamicheskie sistemy i modeli biologii (Dynamical systems and models in biology). Moscow: Fizmatlit; 2010. 400 p. (in Russ.).
- Riznichenko G.Yu. Lektsii po matematicheskim modeliam v biologii (Lectures on Mathematical Models in Biology). Part 1. Moscow-Izhevsk: Scientific Research Center “Regular and Chaotic Dynamics”; 2002. 231 p. (in Russ.).
- Svirezhev Yu.M., Logofet D.O. Stability of Biological Communities. Moscow: Mir; 1983. 324 p.
- Pliusnina T.Yu., Fursova P.V., Terlova L.D., Riznichenko G.Yu. Matematicheskie modeli v biologii (Mathematical Models in Biology). Moscow-Izhevsk: Scientific Research Center “Regular and Chaotic Dynamics”; 2014. 136 p. (in Russ.).
- Nedorezov L.V. Analysis of pine looper population dynamics using discrete time mathematical models. Mathematical Biology and Bioinformatics. 2010;5(2):114–123 (in Russ.). doi: 10.17537/2010.5.114
- Sidorin A.P. Behavior of populations with several stationary states in a random environment. In: Matematicheskie modeli v ekologii i genetike (Mathematical Models in Ecology and Genetics). Moscow; 1981. P. 71–74 (in Russ.).
- Neverova G.P., Frisman E.Ya. Dynamic regimes of local homogeneous population with delayed density dependence. Mathematical Biology and Bioinformatics. 2015;10(2):309–324 (in Russ.). doi: 10.17537/2015.10.309
- Frisman E.Ya., Neverova G.P., Kulakov M.P., Zhigalskii O.A. Changing the Dynamic Modes in Populations with Short Life Cycle: Mathematical Modeling and Simulation. Mathematical Biology and Bioinformatics. 2014;9(2):414–429 (in Russ.). doi: 10.17537/2014.9.414
- Li J. Discrete-time models with mosquitoes carrying genetically-modified bacteria. Mathematical Biosciences. 2012;240(1):35–44. doi: 10.1016/j.mbs.2012.05.012
- Bazykin A.D. Nonlinear Dynamics of Interacting Populations. World Scientific, Singapure; 1998. 193 p. doi: 10.1142/2284
- Iumagulov M.G. Vvedenie v teoriiu dinamicheskikh sistem (Introduction to the theory of dynamical systems). Saint Petersburg; 2015. 272 p. (in Russ.).
- Ricker W.E. Stock and recruitment. J. Fish. Res. Board of Canada. 1954;11(5):559–623. doi: 10.1139/f54-039
- Deych A.M. Metody identifikatsii dinamicheskikh ob''ektov (Methods of identification of dynamic objects). Moscow: Energiya; 1979. 240 p. (in Russ.).
- Ljung L. Identifikatsiia sistem. Teoriia dlia pol'zovatelia. Moscow; 1991. 432 p. (Translation of: Ljung L. System Identification: Theory for the user. Prentice Hall. 1987).
- Shlufman K.V., Neverova G.P., Frisman E.Ya. Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability. Nelin. Dinam. 2016;12(4):553–565 (in Russ.). doi: 10.20537/nd1604001
- Ashikhmina E.V., Izrailsky Yu.G., Frisman E.Ya. Dynamics of the Ricker model with periodical parameter variation. Vestnik of the Far East Branch of the Russian Academy of Sciences. 2004;5:19–28 (in Russ.).
- Sacker R.J., von Bremen H.F. A conjecture on the stability of the periodic solutions of Ricker’s equation with periodic parameters. Appl. Math. Comput. 2010;217(3):1213–1219. doi: 10.1016/j.amc.2010.05.049
- Shlufman K.V., Fishman B.E., Frisman E.Ya. Features of modes for one-dimensional model of Ricker. Izvestiya VUZ. Applied Nonlinear Dynamics. 2012;20(2):12–28 (in Russ.).
- Draper N., Smith H. Prikladnoi regressionnyi analiz. Moscow; 1986. V. 1. 366 p. (Translation of: Draper N., Smith H. Applied regression analysis. John Wiley and Sons; 1981).
- Kosarev M.N., Iumaguzhin F.G., Nugumanov R.G. In: Ispol'zovanie biologicheski aktivnykh produktov pchelovodstva v zhivotnovodstve i veterinarnoi meditsine (Use of biologically active beekeeping products in cattle breeding and veterinary medicine): Scientific Reports. Moscow-Ufa; 1999. P. 118–121 (in Russ.).
- Sharipov A.Ia., Ishbirdin A.R. In: Problemy populiatsionnoi ekologii: Materialy vserossiiskogo seminara «Gomeostaticheskie mekhanizmy biologicheskikh sistem» (Problems of Population Ecology. Proceedings of All-Russia Seminar “Homeostatic mechanisms of biological systems”). Ed. G.S. Rosenberg. Tolliatti; 2015. P. 336–341 (in Russ.).
- Sharipov A.Ya. The influence of climate variations to the state of burzyansk bees. Vestnik of the Orenburg State University. 2010;12:78–81 (in Russ.).
- Vitinsky Yu.I., Kopetsky M., Kuklin G.V. Statistika piatnoobrazovatel'noi deiatel'nosti Solntsa (Sunspot Formation Statistics). Moscow: Nauka; 1986. 296 p. (in Russ.).
