Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control

It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent dynamics for two main reasons: nonlinear recurrent networks often exhibit chaotic behavior and most known learning rules do not work in robust fashion in recurrent networks. Here we address both these problems by demonstrating how random recurrent networks (RRN) that initially exhibit chaotic dynamics can be tuned through a supervised learning rule to generate locally stable neural patterns of activity that are both complex and robust to noise. The outcome is a novel neural network regime that exhibits both transiently stable and chaotic trajectories. We further show that the recurrent learning rule dramatically increases the ability of RRNs to generate complex spatiotemporal motor patterns, and accounts for recent experimental data showing a decrease in neural variability in response to stimulus onset

Onset Mechanisms and Anomalous Diffusion Phenomena of Strange Nonchaotic Attractors

制度:新 ; 報告番号:甲3305号 ; 学位の種類:博士(理学) ; 授与年月日:2011/2/25 ; 早大学位記番号:新560

Parametric Feedback Resonance in Chaotic Systems

If one changes the control parameter of a chaotic system proportionally to the distance between an arbitrary point on the strange attractor and the actual trajectory, the lifetime τ of the most stable unstable periodic orbit in the vicinity of this point starts to diverge with a power law. The volume in parameter space where τ becomes infinite is finite and from its nonfractal boundaries one can determine directly the local Liapunov exponents. The experimental applicability of the method is demonstrated for two coupled diode resonators

A simple method for detecting chaos in nature

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available

Spontaneous Synchronization in Two Mutually Coupled Memristor-Based Chua’s Circuits: Numerical Investigations

Chaotic dynamics of numerous memristor-based circuits is widely reported in literature. Recently, some works have appeared which study the problem of synchronization control of these systems in a master-slave configuration. In the present paper, the spontaneous dynamic behavior of two chaotic memristor-based Chua’s circuits, mutually interacting through a coupling resistance, was studied via computer simulations in order to study possible self-organized synchronization phenomena. The used memristor is a flux controlled memristor with a cubic nonlinearity, and it can be regarded as a time-varying memductance. The memristor, in effect, retains memory of its past dynamic and any difference in the initial conditions of the two circuits results in different values of the corresponding memductances. In this sense, due to the memory effect of the memristor, even if coupled circuits have the same parameters they do not constitute two completely identical chaotic oscillators. As is known, for nonidentical chaotic systems, in addition to complete synchronizations (CS) other weaker forms of synchronization which provide correlations between the signals of the two systems can also occur. Depending on initial conditions and coupling strength, both chaotic and nonchaotic synchronization are observed for the system considered in this work