A chaotic network of size $N$ with delayed interactions which resembles a pseudo-inverse associative memory neural network is investigated. For a load $α=P/N<1$, where $P$ stands for the number of stored patterns, the chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with $α$. At finite $α$, a chaotic spin glass phase exists, where the number of distinct chaotic attractors scales exponentially with $N$. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the $N$ chaotic units or freezing with respect to the $P$ patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.
Experimental observation of chaotic and multistable dynamics in a Duffing--Holmes--type analog circuit: antiperiodicity and attractor-coexistence signatures
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of chaos. In particular a cusp bifurcation of periodic orbits and resulting branches of folds of periodic orbits effectively partition the parameter space into regions where different behaviours are seen. The cusp bifurcation leads directly to bistability between periodic orbits, and subsequently to bistability between a periodic orbit and a chaotic attractor. Th…
University College Cork（科克大学学院）；Ludwig-Maximilians University Munich（慕尼黑路德维希-马克西米利安大学）；Collins Aerospace（柯林斯航空航天公司）；Deutsches Zentrum für Luft-und Raumfahrt（德国航空航天中心）
Multifunctional neural networks are capable of performing more than one task without changing any network connections. In this paper we explore the performance of a continuous-time, leaky-integrator, and next-generation `reservoir computer' (RC), when trained on tasks which test the limits of multifunctionality. In the first task we train each RC to reconstruct a coexistence of chaotic attractors from different dynamical systems. By moving the data describing these attractors closer together, we find that the extent to which each RC can reconstruct both attractors diminishes as they begin to o…
In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective Lyapunov exponents. Our results from bifurcations and the largest Lyapunov exponent show bistable dynamics for all the parameters of the model. Choosing the inverse of latent period as control parameter, over 70% of the interval comprises the coexistence of periodic and chaotic attractors, bistable dynamics. Despite the competition between these attractors, the ch…
