"A simplified model of natural convection, similar to the Lorenz (1963) system, is compared to computational fluid dynamics simulations in order to test data assimilation methods and better understand the dynamics of convection. The thermosyphon is represented by a long time flow simulation, which serves as a reference "truth". Forecasts are then made using the Lorenz-like model and synchronized to noisy and limited observations of the truth using data assimilation. The resulting analysis is observed to infer dynamics absent from the model when using short assimilation windows.

Furthermore, chaotic flow reversal occurrence and residency times in each rotational state are forecast using analysis data. Flow reversals have been successfully forecast in the related Lorenz system, as part of a perfect model experiment, but never in the presence of significant model error or unobserved variables. Finally, we provide new details concerning the fluid dynamical processes present in the thermosyphon during these flow reversals."

"Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a non-monotonic function of stimulus frequency, revealing a "resonant" frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate."

"Although Laposky, a draftsman by profession, had received a proper recognition as a pioneer of electronic art, at no time his name has emerged in the context of dynamical chaos theory. The circuits he had implemented for generation of “oscillons” on the screen of a cathode ray tube oscilloscope, remain a mystery. It is known that some of his thirty-seven circuits [2] had “as many as 70 different setting of controls”[3] and that ac-voltage has been used for the circuit feeding. Our analysis is based on the vanity press booklet with the still photos of the fifty-six oscillons, which were exhibited at the Sanford Museum (Cherokee, Iowa) in 1953 [2]."

"This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is based on the continuous wavelet transform and the wavelet multiresolution analysis. A new parameter, the \textit{scale index}, is introduced and interpreted as a measure of the degree of the signal's non-periodicity. This methodology is successfully applied to three classical dynamical systems: the Bonhoeffer-van der Pol oscillator, the logistic map, and the Henon map."

"Much recent interest has focused on "open" dynamical systems, in which a classical map or flow is considered only until the trajectory reaches a "hole", at which the dynamics is no longer considered. Here we consider questions pertaining to the survival probability as a function of time, given an initial measure on phase space. We focus on the case of billiard dynamics, namely that of a point particle moving with constant velocity except for mirror-like reflections at the boundary, and give a number of recent results, physical applications and open problems."

"WOB combines a database of bifurcation problems with a tutorial on nonlinear phenomena.

WOB is designed to be part of a virtual university. The approach is example-oriented and experimental. The emphasis is on examples that are application-oriented."

via: Making Light