Nets: Punctuated Evolution

[James Brody]

Instead of wiping the slate blank, psychiatry often looks to evolution to underlay beliefs and labels already in use. It could be that network simulations can make a similar error. Or it could be that what we already know is correct and, therefore, we should expect a close alignment to whatever we make up next week.

JimB

Punctuated Evolution due to Delayed Carrying Capacity
V.I. Yukalov E.P. Yukalova and D. Sornette

Abstract

A new logistic delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classificationof 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 logistic 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, moving finite-time singularities as well as finite-time death.

More at http://arxiv.org/PS_cache/arxiv/pdf/...901.4714v1.pdf