2009/01/31 by V. I. Yukalov, E. P. Yukalova, D. Sornette +1 · 1 citation
Mathematics · Medicine · Physics and Astronomy · Social Sciences · #Advanced Thermodynamics and Statistical Mechanics #Biology #Bistability #Competition (biology) #Demography #Ecology #Evolutionary Game Theory and Cooperation #Exponential growth #Geology #Gravitational singularity #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Mechanics #Monotonic function #Nonlinear system #Physics #Population #Punctuated equilibrium #Quantum mechanics #Statistical physics #nlin.AO #physics.bio-ph #physics.soc-ph
paper · pdf · doi:10.1016/j.physd.2009.05.011
published as Physica D 238 (2009) 1752-1767 · Latex file, 58 pages, 29 figures. Published variant
openalex publication_date 2009/06/12 · arxiv created 2009/08/10 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.