Abstract
This paper shows the possibility of solving the problem of the transition between periodic and point attractors in the bistable Rosenzweig–MacArthur model with modifications for the dynamics of root hemiparasitic plants and their hosts.
REFERENCES
V. V. Aleksandrov, T. B. Aleksandrova, L. L. Cruzado, and R. J. A. Escamilla, ‘‘Controlled transition in a model of biomass dynamics of root hemiparasitic plants,’’ Moscow Univ. Mech. Bull. 76, 111–117 (2021). https://doi.org/10.3103/s0027133021040026
P. Fibich, J. Lepš, and L. Berec, ‘‘Modelling the population dynamics of root hemiparasitic plants along a productivity gradient,’’ Folia Geobot. 45, 425–442 (2010). https://doi.org/10.1007/s12224-010-9080-7
S. Habimana, A. Nduwumuremyi, and R. J. D. Chinama, ‘‘Management of Orobanche in field crops: A review,’’ J. Soil Sci. Plant Nutr. 14 (1), 43–62 (2014). https://doi.org/10.4067/s0718-95162014005000004
E. Simiu, Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Applications of Melnikov Processes in Engineering, Physics, and Neuroscience, Princeton Series in Applied Mathematics, Vol. 26 (Princeton Univ. Press, Princeton, N.J., 2002). https://doi.org/10.1515/9781400832507
V. V. Aleksandrov, T. B. Aleksandrova, I. S. Konovalenko, and K. V. Tikhonova, ‘‘Perturbed stable systems on a plane. Part 2,’’ Moscow Univ. Mech. Bull. 72, 19–22 (2017). https://doi.org/10.3103/s0027133017010046
I. S. Konovalenko, ‘‘On construction of an attainability set in the neighborhood of a periodic attractor,’’ Moscow Univ. Mech. Bull. 75, 80–85 (2020). https://doi.org/10.3103/S0027133020030048
B. E. Beisner, D. T. Haydon, and K. Cuddington, ‘‘Alternative stable states in ecology,’’ Front. Ecol. Environ. 1, 376–382 (2003). https://doi.org/10.1890/1540-9295(2003)001[0376:assie]2.0.co;2
V. N. Zhermolenko, ‘‘B.V. Bulgakov’s problem on the maximum deflection of a second-order oscillating system,’’ Vestn. Mosk. Univ.: Mat. Mekh., No. 3, 87–91 (1980).
J. Hershenhorn, E. Dor, B. Alperin, R. Lati, H. Eizenberg, T. Lande, G. Acdary, S. Graph, Y. Kapulnik, and S. Vininger, ‘‘Integrated broomrape control — Resistant lines, chemical and biological control and sanitation — Can we combine them together?,’’ in Workshop Parasitic Plant Management in Sustainable Agriculture; Final Meeting of COST849 (ITQB Oeiras, Lisbon, 2006), pp. 23–24.
C. Alister and M. Kogan, ‘‘Efficacy of imidazolinone herbicides applied to imidazolinone-resistant maize and their carryover effect on rotational crops,’’ Crop Prot. 24, 375–379 (2005). https://doi.org/10.1016/j.cropro.2004.09.011
M. S. Dinesha, G. N. Dhanapal, D. Prabhudev, N. S. Vignesh, V. Madhukumar, and K. Raghavendra, ‘‘Efficiency and economics of broomrape (Orobanche cernua Loefl.) control with herbicides in infested tomato (Lycopersicon esculentum Mill.) field,’’ Plant Arch. 12, 833–836 (2012).
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Translated by E. Oborin
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Cruzado Lima, L., Aleksandrov, V.V., Netzahualcoyotl Bautista, C. et al. Controlled Transition in a Modified Model of Biomass Dynamics of Root Hemiparasitic Plants. Moscow Univ. Mech. Bull. 79, 6–11 (2024). https://doi.org/10.3103/S0027133024700018
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DOI: https://doi.org/10.3103/S0027133024700018