Skip to main content
SpringerLink
Log in

Continuous Model for the Devastating Oscillation Dynamics of Local Forest Pest Populations in Canada*

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

A sharp and prolonged change in developing population processes requires mathematical methods to be improved. Unusual phase changes in the development of mass reproduction of insect species stipulated the idea to develop a new model in which not the final form of an asymptotically stable state after bifurcations but transient modes are of importance. In concrete situations, it is proposed to consider the phenomena, which are identified with population outbreaks (non-stationary heterogeneous processes) in environmental studies, within the context of a long oscillatory mode only as peaks of the phases of sharp nonharmonic oscillations. The proposed new dynamic model in the form of a differential equation describes a decreasing pseudoperiodic damping trajectory of sudden sharp oscillations that implement a non-bifurcation scenario of spontaneous completion for a particular variant of mass forest pest reproduction. Situations in two provinces of eastern Canada are considered as examples.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. I. Vorontsov, Forest Entomology [in Russian], Ecologia, Moscow (1995).

    Google Scholar 

  2. J. R. Blais, “Spruce budworm outbreaks in the lower St. Lawrence and Gaspe regions,” The Forestry Chronicle, Vol. 37, No. 3, 192–202 (1961).

    Article  Google Scholar 

  3. A. Y. Perevaryukha, “Modeling abrupt changes in population dynamics with two threshold states,” Cybernetics and Systems Analysis, Vol. 52, No. 4, 623–630 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  4. L. R. Clark, “The population dynamics of Cardiaspina albitextura (Psyllidae),” Australian Journal of Zoology, Vol. 12, No. 3, 362–380 (1964).

    Article  Google Scholar 

  5. W. C. Allee and E. Bowen, “Studies in animal aggregations: Mass protection against colloidal silver among goldfishes,” Journal of Experimental Zoology, Vol. 61, No. 2, 185–207 (1932).

    Article  Google Scholar 

  6. A. A. Hall, Ecology and Evolution of Cardiaspina Psyllids, Their Bacterial Endosymbionts and Parasitoid Wasps, Thesis Submitted in Fulfilment of the Requirements for the Degree of Doctor of Philosophy, Western Sydney University (2016).

  7. J. Berry, “Brown lace lerp hyperparasitoid found in New Zealand,” Biosecurity New Zealand, Iss. 68, 18–20 (2006).

    Google Scholar 

  8. B. Cooke, S. V. Neali, and J. Regniere, “Insect defoliators as periodic disturbances in northern forest ecosystems,” in: Plant Disturbance Ecology: The Process and the Response, Elsevier, Burlington (2007), pp. 487–525.

    Google Scholar 

  9. T. Royama, “Population dynamics of the spruce budworm,” Choristoneura Fumiferana, Ecological Monographs, Vol. 54, No. 4, 429–462 (1984).

    Article  Google Scholar 

  10. ESTR Secretariat Atlantic Maritime Ecozone evidence for key findings summary. Canadian biodiversity: Ecosystem status and trends 2010. Evidence for Key Findings Summary Report 2014. No. 3. Ottawa, ON: Canadian Councils of Resource Ministers.

  11. M. R. Rose and R. Harmsen, “Ecological outbreak dynamics and the cusp catastrophe,” Acta Biotheoretica, Vol. 30, 229–253 (1981).

    Article  Google Scholar 

  12. T. Poston and I. Stewart, Catastrophe Theory and Its Applications, Pitman Publishing Limited, London (1978).

    MATH  Google Scholar 

  13. D. R. Brillinger, “The Nicholson blowfly experiments: Some history and EDA,” Journal of Time Series Analysis, Vol. 33, Iss. 5, 718–723 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  14. G. Hutchinson, “Circular causal systems in ecology,” Annals of the New York Academy of Sciences, Vol. 50, Iss. 4, 221–246 (1948).

    Article  Google Scholar 

  15. B. D. Hassard, N. D. Kazarinoff, and Y.-H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge (1981).

    MATH  Google Scholar 

  16. S. A. Gourley, J. W. So, and J. H. Wu, “Nonlocality of reaction-diffusion equations induced by delay: Biological modeling and nonlinear dynamics,” Journal of Mathematical Sciences, Vol. 124, Iss. 4, 5119–5153 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  17. K. Gopalsamy, M. Kulenovic, and G. Ladas, “Time lags in a ”food-limited “population model”, Applicable Analysis, Vol 31, Iss. 3, 225–237 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Milnor, “On the concept of attractor: Correction and remarks,” Comm. Math. Phys., Vol. 102, No. 3, 517–519 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  19. D. Ludwig, D. D. Jones, and C. S. Holling, “Qualitative analysis of insect outbreak systems: The spruce budworm and forest,” Journal of Animal Ecology, Vol. 47, No. 1, 315–332 (1978).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg Institute for Informatics and Automation, Russian Academy of Sciences, St. Petersburg, Russia

    A. Yu. Perevaryukha

Authors
  1. A. Yu. Perevaryukha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Yu. Perevaryukha.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2019, pp. 164–177.

*This work was performed within the projects No. 18-04-00399 (VIZR) and No. 17-07-00125 (SPIIRAN) of the Russian Foundation for Basic Research.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Perevaryukha, A.Y. Continuous Model for the Devastating Oscillation Dynamics of Local Forest Pest Populations in Canada*. Cybern Syst Anal 55, 141–152 (2019). https://doi.org/10.1007/s10559-019-00119-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-019-00119-6

Keywords

Search

Navigation