caa a22 4500 467893276 CHVBK 20180406152755.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s10955-006-9232-6 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9232-6 Probability of Local Bifurcation Type from a Fixed Point: A Random Matrix Perspective [Elektronische Daten] [D. Albers, J. Sprott] Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectrum is considered both numerically and analytically using previous work of Edelman et al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion does not hold, e.g., real random matrices with Gaussian elements with a large positive mean and finite variance. Springer Science+Business Media, LLC, 2006 dynamical systems nationallicence structural stability nationallicence stability conjecture nationallicence Lyapunov exponents nationallicence complex systems nationallicence routes to chaos nationallicence random matrices nationallicence bifurcation theory nationallicence Albers D. Max Planck Institute for Mathematics in the Sciences, D-04103, Leipzig, Germany aut Sprott J. Physics Department, University of Wisconsin, 53706, Madison, WI, USA aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/4(2006-11-01), 885-921 0022-4715 125:4<885 2006 125 10955 https://doi.org/10.1007/s10955-006-9232-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9232-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Albers D. Max Planck Institute for Mathematics in the Sciences, D-04103, Leipzig, Germany aut NATIONALLICENCE 700 1- Sprott J. Physics Department, University of Wisconsin, 53706, Madison, WI, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/4(2006-11-01), 885-921 0022-4715 125:4<885 2006 125 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer