Dynamic modes of exploited limited population: results of modeling and numerical study

G. P. Neverova ; A. I. Abakumov ; E. Ya. Frisman

Matematičeskaâ biologiâ i bioinformatika, Tome 11 (2016) no. 1, pp. 1-13.

Résumé

The paper investigates the model of population dynamics with age structure and density dependence of birth rate. We consider two situations: 1) the population develops freely and 2) the population is exploited. It was shown that harvesting leads to the stabilization of the dynamics. There is multiregimism, i.e. different dynamic regimes are possible with the same values of demographic parameters. It is shown that even a single harvesting in the current population size could lead to a change of the observed dynamic regime.

Bibliographie

[1] Skaletskaya E. I., Frisman E. Ya., Shapiro A. P., Diskretnye modeli chislennosti populyatsii i optimizatsiya promysla, Nauka, M., 1979, 165 pp.

[2] Abakumov A. I., Upravlenie i optimizatsiya v modelyakh ekspluatiruemykh populyatsii, Dalnauka, Vladivostok, 1993, 129 pp.

[3] Abakumov A. I., “Optimalnyi sbor urozhaya v modelyakh populyatsii”, Obozrenie prikladnoi i promyshlennoi matematiki, 1:6 (1994), 834–849 | Zbl

[4] Tyutyunov Yu. V., Dombrovskii Yu. A., Obuschenko N. I., “Optimalnoe upravlenie ekspluatiruemoi populyatsiei pri minimizatsii riska ee vymiraniya v usloviyakh stokhastichnosti sredy”, Obozrenie prikladnoi i promyshlennoi matematiki, 3:3 (1994), 412–433

[5] Srinivasu P. D. N., Ismail S., “Global dynamics and controllability of a harvested prey-predator system”, Journal of Biological Systems, 9:1 (2001), 67–79 | DOI

[6] Braumann C. A., “Variable effort harvesting models in random environments: generalization to density-dependent noise intensities”, Mathematical Biosciences, 177–178 (2002), 229–245 | DOI | MR | Zbl

[7] Frisman E. Ya., Last E. V., “Nelineinye effekty v populyatsionnoi dinamike, svyazannye s vozrastnoi strukturoi i vliyaniem promysla”, Izvestiya RAN. Seriya biologicheskaya, 2005, no. 5, 517–530 | Zbl

[8] Zhdanova O. L., Kolbina E. A., Frisman E. Ya., “Vliyanie promysla na geneticheskoe raznoobrazie i kharakter dinamicheskogo povedeniya mendelevskoi limitirovannoi populyatsii”, Doklady Akademii nauk, 412:4 (2007), 564–567

[9] Ilin O. I., “Ob optimalnoi ekspluatatsii populyatsii ryb s vozrastnoi strukturoi”, Sibirskii zhurnal industrialnoi matematiki, 10:3 (2007), 43–57 | Zbl

[10] Abakumov A. I., Ilin O. I., Ivanko N. S., “Igrovye zadachi sbora urozhaya v biologicheskom soobschestve”, Matematicheskaya teoriya igr i ee prilozheniya, 3:2 (2011), 3–17

[11] Abakumov A. I., “Optimalnoe upravlenie populyatsiei s raspredelennymi parametrami”, Informatika i sistemy upravleniya, 2011, no. 3, 3–9

[12] Rojas-Palma A., González-Olivares E., “Optimal harvesting in a predator-prey model with Allee effect and sigmoid functional response”, Applied Mathematical Modelling, 36 (2012), 1864–1874 | DOI | MR | Zbl

[13] Zhdanova O. L., Frisman E. Ya., “Vliyanie optimalnogo promysla na kharakter dinamiki chislennosti i geneticheskogo sostava dvukhvozrastnoi populyatsii”, Izvestiya RAN. Seriya biologicheskaya, 2013, no. 6, 738–749 | DOI | Zbl

[14] Saucedo-Solorio J. M., Pisarchik A. N., Aboites V., “Shift of critical points in the parametrically modulated Henon map with coexisting attractors”, Physics Letters A, 304 (2002), 21–29 | DOI | MR | Zbl

[15] Pisarchik A. N., Feudel U., “Control of multistability”, Physics Reports, 540 (2014), 167–218 | DOI | MR

[16] Frisman E. Ya., Neverova G. P., Kulakov M. P., Zhigalskii O. A., “Smena dinamicheskikh rezhimov v populyatsiyakh vidov s korotkim zhiznennym tsiklom: rezultaty analiticheskogo i chislennogo issledovaniya”, Matematicheskaya biologiya i bioinformatika, 9:2 (2014), 414–429 | DOI

[17] Frisman E. Ya., Neverova G. P., Kulakov M. P., Zhigalskii O. A., “Yavlenie multirezhimnosti v populyatsionnoi dinamike zhivotnykh s korotkim zhiznennym tsiklom”, Doklady Akademii nauk, 460:4 (2015), 488–493 | DOI

[18] Shapiro A. P., “Rol plotnostnoi regulyatsii v vozniknovenii kolebanii chislennosti mnogovozrastnoi populyatsii”, Issledovaniya po matematicheskoi populyatsionnoi ekologii, DVNTs AN SSSR, Vladivostok, 1983, 3–17

[19] Frisman E. Ya., Luppov S. P., Skokova I. N., Tuzinkevich A. V., “Slozhnye rezhimy dinamiki chislennosti populyatsii, predstavlennoi dvumya vozrastnymi klassami”, Matematicheskie issledovaniya v populyatsionnoi ekologii, DVO AN SSSR, Vladivostok, 1988, 4–18

[20] Frisman E. Ya., “Strannye attraktory v prosteishikh modelyakh dinamiki chislennosti populyatsii s vozrastnoi strukturoi”, Doklady Rossiiskoi akademii nauk, 338:2 (1994), 282–286 | Zbl

[21] Frisman E. Ya., Neverova G. P., Revutskaya O. L., Kulakov M. P., “Rezhimy dinamiki modeli dvukhvozrastnoi populyatsii”, Izv. vuzov. PND, 18:2 (2010), 111–130

[22] Frisman E. Ya., Neverova G. P., Revutskaya O. L., “Complex Dynamics of the Population with a Simple Age Structure”, Ecological Modelling, 222 (2011), 1943–1950 | DOI

[23] Ricker W. E., “Stock and recruitment”, J. Fish. Res. Board of Canada, 11:5 (1954), 559–623 | DOI