Punctuated Evolution due to Delayed Carrying Capacity

V.I. Yukalov, E.P. Yukalova and D. Sornette ()

No CCSS-09-004, Working Papers from ETH Zurich, Chair of Systems Design

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 (search for similar items in EconPapers)
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