http://people.physik.hu-berlin.de/~lindner/PDF/physreport.pdf

Effects of noise in excitable systems

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, but 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 nonmonotonic 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.

/pdf/stimulus-dependent-suppression-of-chaos-in-recurrent-neural-12ndqgtpgh.pdf

Stimulus-dependent suppression of chaos in recurrent neural networks

Stochastic theory of nonequilibrium steady states and its applications. Part I

Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.

/pdf/nonlinear-systems-in-medicine-1q5e0meq16.pdf

Nonlinear Systems in Medicine

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast–slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities (stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.). Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Integer multiple spiking in neuronal pacemakers without external periodic stimulation

Burst and coherence resonance in Rose–Hindmarsh model induced by additive noise

The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a carrier steady wave and its perturbation, we find that the controlling mechanism can be explained by a slaving principle. The critical controlling time for a perturbation mode increases exponentially with its wave number.

Controlling spatiotemporal chaos via small external forces

Controlling spatio-temporal chaos via small external forces

The complexity of a nonlinear dynamic system can be suppressed by adding an external period force with appropriate choice of frequency and amplitude directly on the slowly changing variable of the system. Numerical results indicate that the method not only can suppress chaos but also is robust to the additive external noise.

Shunguang Wu

Papers

Integer multiple spiking in neuronal pacemakers without external periodic stimulation

Burst and coherence resonance in Rose–Hindmarsh model induced by additive noise

Controlling spatiotemporal chaos via small external forces

Controlling spatio-temporal chaos via small external forces

Suppressing complexity via the slaving principle