RUS  ENG
Full version
JOURNALS // Matematicheskaya Biologiya i Bioinformatika

Mat. Biolog. Bioinform., 2019, Volume 14, Issue 2, Pages 588–611 (Mi mbb405)

Synchronization and bursting activity in the model for two predator-prey systems coupled by predator migration
M. P. Kulakov, E. V. Kurilova, E. Ya. Frisman

References

1. E. Ya. Frisman, M. P. Kulakov, O. L. Revutskaya, O. L. Zhdanova, G. P. Neverova, “Osnovnye napravleniya i obzor sovremennogo sostoyaniya issledovanii dinamiki strukturirovannykh i vzaimodeistvuyuschikh populyatsii”, Kompyuternye issledovaniya i modelirovanie, 11:1 (2019), 119–151  mathnet  crossref  mathscinet  scopus
2. B. Mukhopadhyay, R. Bhattacharyya, “Role of predator switching in an eco-epidemiological model with disease in the prey”, Ecological Modelling, 220:7 (2009), 931–939  crossref  scopus
3. Md. Saifuddin, S. Biswas, S. Samanta, S. Sarkar, J. Chattopadhyay, “Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator”, Chaos, Solitons & Fractals, 91 (2016), 270–285  crossref  mathscinet  zmath  scopus
4. H. N. Comins, M. P. Hassell, R. M. May, “The spatial dynamics of host-parasitoid systems”, J. Animal Ecology, 61 (1992), 735–748  crossref  scopus
5. V. N. Govorukhin, A. B. Morgulis, Yu. V. Tyutyunov, “Medlennyi taksis v modeli khischnik-zhertva”, Doklady Akademii nauk, 372:6 (2000), 730–732  mathnet  zmath
6. Yu. V. Tyutyunov, L. I. Titova, I. N. Senina, “Prey-taxis destabilizes homogeneous stationary state in spatial Gause-Kolmogorov-type model for predator-prey system”, Ecological Complexity, 31 (2017), 170–180  crossref  elib  scopus
7. V. Křivan, J. Eisner, “The effect of the Holling type II functional response on apparent competition”, Theoretical Population Biology, 70 (2006), 421–430  crossref  scopus
8. Y. Shen, Z. Hou, H. Xin, “Transition to burst synchronization in coupled neuron networks”, Physical Review E, 77 (2008), 031920, 1–5  crossref  scopus
9. Yu. V. Bakhanova, A. O. Kazakov, A. G. Korotkov, “Spiralnyi khaos v modelyakh tipa Lotki-Volterry”, Zhurnal srednevolzhskogo matematicheskogo obschestva, 19:2 (2017), 13–24  mathnet  crossref  zmath
10. Y. V. Bakhanova, A. O. Kazakov, A. G. Korotkov, T. A. Levanova, G. V. Osipov, “Spiral attractors as the root of a new type of “bursting activity” in the Rosenzweig-MacArthur model”, Eur. Phys. J. Special, 227 (2018), 959–970  crossref  scopus
11. T. Huang, H. Zhang, “Bifurcation, chaos and pattern formation in a space-and time-discrete predator-prey system”, Chaos, Solitons & Fractals, 91 (2016), 92–107  crossref  mathscinet  zmath  scopus
12. E. M. Izhikevich, “Neural excitability, spiking, bursting”, International Journal of Bifurcation and Chaos, 10:06 (2000), 1171–1266  crossref  mathscinet  zmath  scopus
13. E. M. Izhikevich, “Synchronization of Elliptic Bursters”, SIAM REVIEW, 43:2 (2001), 315–344  crossref  mathscinet  zmath  scopus
14. A. Shilnikov, G. Cymbalyuk, “Homoclinic bifurcations of periodic orbits en a route from tonic-spiking to bursting in neuron models”, Regular and Chaotic Dynamics, 9:3 (2004), 281–297  mathnet  crossref  mathscinet  zmath  scopus
15. V. N. Belykh, I. V. Belykh, M. Colding-Jørgensen, E. Mosekilde, “Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models”, Eur. Phys. J. E, 2000, no. 3, 205–219  crossref  scopus
16. M. Kolomiets, A. Shilnikov, “Metody kachestvennoi teorii dlya modeli Khindmarsh-Rouz”, Nelineinaya dinamika, 6:1 (2010), 23–52  mathnet  crossref
17. V. A. A. Jansen, “The Dynamics of Two Diffusively Coupled Predator-Prey Populations”, Theoretical Population Biology, 59:2 (2001), 119–131  crossref  zmath  scopus
18. Y. Liu, The Dynamical Behavior of a Two Patch Predator-Prey Model, Theses, Dissertations, & Master Projects, 2010, 46 pp.
19. S. Saha, N. Bairagi, S. K. Dana, “Chimera states in ecological network under weighted mean-field dispersal of species”, Front. Appl. Math. Stat., 5:15 (2019), 1–11  crossref  scopus
20. A. D. Bazykin, Matematicheskaya biofizika vzaimodeistvuyuschikh populyatsii, Nauka, M., 1985, 182 pp.  mathscinet
21. A. D. Bazykin, Nonlinear Dynamics of Interacting Populations, eds. A. I. Khibnik, B. Krauskopf, World Scientific Publishing Co. Pte. Ltd, 1998, 216 pp.  crossref  mathscinet
22. S. Rinaldi, S. Muratori, “Slow-fast limit cycles in predator-prey models”, Ecological Modelling, 61 (1992), 287–308  crossref  scopus
23. E. V. Kurilova, M. P. Kulakov, E. Ya. Frisman, “Posledstviya sinkhronizatsii kolebanii chislennostei v dvukh vzaimodeistvuyuschikh soobschestvakh tipa «khischnik–zhertva» pri nasyschenii khischnika i limitirovanii chislennosti zhertvy”, Informatika i sistemy upravleniya, 45:3 (2015), 24–34
24. C. S. Holling, “Some characteristics of simple types of predation and parasitism”, Canadian Entomologist, 91 (1959), 385–398  crossref  scopus
25. S. Ghosh, S. Bhattacharyya, “A two-patch prey-predator model with food-gathering activity”, J. Appl. Math. Comput., 37 (2011), 497–521  crossref  mathscinet  zmath  scopus
26. Y. Kang, S. K. Sasmal, K. Messan, “A two-patch prey-predator model with predator dispersal driven by the predation strength”, Mathematical Biosciences and Engineering, 14:4 (2017), 843–880  crossref  mathscinet  zmath  scopus
27. E. V. Kurilova, M. P. Kulakov, “Slozhnye rezhimy v modeli migratsionno svyazannykh soobschestv «khischnik-zhertva» s bystrymi i medlennymi tsiklami”, Regionalnye problemy, 22:1 (2019), 12–19  crossref
28. T. Asada, H. Yoshida, “Coefficient criterion for four-dimensional Hopf bifurcations: a complete mathematical characterization and applications to economic dynamics”, Chaos, Solitons and Fractals, 18 (2003), 525–536  crossref  mathscinet  zmath  scopus
29. A. Dhooge, W. Govaerts, Yu. A. Kuznetsov, H. G. E. Meijer, B. Sautois, “New features of the software MatCont for bifurcation analysis of dynamical systems”, Mathematical and Computer Modelling of Dynamical Systems, 14:2 (2008), 147–175  crossref  mathscinet  zmath  scopus
30. E. Benoît, J. L. Callot, F. Diener, M. Diener, “Chasse au canard”, Collectanea Mathematica, 31-32 (1981), 37–119  mathscinet
31. E. K. Ersöz, M. Desroches, C. R. Mirasso, S. Rodrigues, “Anticipation via canards in excitable systems”, Chaos, 013111:29 (2019)  crossref  mathscinet  zmath  scopus
32. N. Fenichel, “Geometric Singular Perturbation Theory for Ordinary Differential Equations”, Journal of Differential Equations, 31 (1979), 53–98  crossref  mathscinet  zmath  scopus
33. M. Desrochesy, V. Kirk, “Spike-Adding in a Canonical Three-Time-Scale Model: Superslow Explosion and Folded-Saddle Canards”, SIAM J. Applied dynamical systems, 17:3 (2018), 1989–2017  crossref  mathscinet  scopus


© Steklov Math. Inst. of RAS, 2026