Skip to main content
Log in

Controlled Transition in a Modified Model of Biomass Dynamics of Root Hemiparasitic Plants

  • Published:
Moscow University Mechanics Bulletin Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

REFERENCES

  1. 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

    Article  Google Scholar 

  2. 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

    Article  Google Scholar 

  3. 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

    Article  Google Scholar 

  4. 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

  5. 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

    Article  Google Scholar 

  6. 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

    Article  Google Scholar 

  7. 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

    Article  Google Scholar 

  8. 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).

  9. 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.

  10. 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

    Article  Google Scholar 

  11. 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).

    Google Scholar 

Download references

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to L. Cruzado Lima, V. V. Aleksandrov, C. Netzahualcoyotl Bautista or O. V. Aleksandrova.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated by E. Oborin

Publisher’s Note.

Allerton Press remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027133024700018

Keywords:

Navigation