Paper: CCSS-09-004

Title: Punctuated Evolution due to Delayed Carrying Capacity

Authors: 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.

Keywords: Delay equations, Population dynamics, Punctuated evolution

Manuscript status: Published

Reference: Physica D Volume: 238, Pages: 1752-1767 (2009)

JEL codes:
PACS numbers: 02.30.Ks, 87.23.Ce, 87.23.Ge, 87.23.Kg, 89.65.Gh

Local copy of the paper: CCSS-09-004.pdf

Submission date: 25-05-2009