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Punctuated Evolution due to Delayed Carrying Capacity

Author

Listed:
  • V.I. Yukalov
  • E.P. Yukalova
  • D. Sornette

Abstract

A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a population in the four main regimes dominated respectively by: (i) gain and competition, (ii) gain and cooperation, (iii) loss and competition and (iv) loss and cooperation. Our delay equation may exhibit bistability in some parameter range, as well as a rich set of regimes, including monotonic decay to zero, smooth exponential growth, punctuated unlimited growth, punctuated growth or alternation to a stationary level, oscillatory approach to a stationary level, sustainable oscillations, finite-time singularities as well as finite-time death.

Suggested Citation

  • V.I. Yukalov & E.P. Yukalova & D. Sornette, "undated". "Punctuated Evolution due to Delayed Carrying Capacity," Working Papers CCSS-09-004, ETH Zurich, Chair of Systems Design.
    • Handle: RePEc:stz:wpaper:ccss-09-004
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    Citations

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    Cited by:

    1. Pati, N.C. & Ghosh, Bapan, 2022. "Delayed carrying capacity induced subcritical and supercritical Hopf bifurcations in a predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 171-196.
    2. Miškinis, Paulius & Vasiliauskienė, Vaida, 2017. "The analytical solutions of the harvesting Verhulst’s evolution equation," Ecological Modelling, Elsevier, vol. 360(C), pages 189-193.
    3. Nguyen Tien, Dung, 2013. "The existence of a positive solution for a generalized delay logistic equation with multifractional noise," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1240-1246.
    4. Cortés, J.-C. & Moscardó-García, A. & Villanueva, R.-J., 2022. "Uncertainty quantification for hybrid random logistic models with harvesting via density functions," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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