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arXiv · 0901.4714

Punctuated evolution due to delayed carrying capacity

V. I. Yukalov·E. P. Yukalova·D. Sornette
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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.

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V. I. Yukalov, E. P. Yukalova, D. Sornette. 2009-01-29. Punctuated evolution due to delayed carrying capacity. https://doi.org/10.1016/j.physd.2009.05.011

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