Punctuated evolution due to delayed carrying capacity
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.
Cite
@article{arxiv.0901.4714,
title = {Punctuated evolution due to delayed carrying capacity},
author = {V. I. Yukalov and E. P. Yukalova and D. Sornette},
journal= {arXiv preprint arXiv:0901.4714},
year = {2015}
}
Comments
Latex file, 58 pages, 29 figures. Published variant