Modeling of Complex Multidimensional Nonlinear Systems Using Neural System with Deep Architectures

2014 ◽  
pp. 127-143
Author(s):  
Bogdan M. Wilamowski ◽  
Janusz Korniak
Keyword(s):  
Nonlinear Systems ◽  
Neural System

Lyapunov Theory-Based Fusion Neural Networks for the Identification of Dynamic Nonlinear Systems

2019 ◽  
Vol 29 (09) ◽  
pp. 1950015 ◽  
Author(s):  
Spyridon Plakias ◽  
Yiannis S. Boutalis
Keyword(s):  
Nonlinear Systems ◽  
Additive Noise ◽  
Learning Algorithm ◽  
Neural System ◽  
Lyapunov Theory ◽  
Identification Process ◽  
Neural Architecture ◽  
Parameter Variations ◽  
Error System ◽  
Task Simulation

This paper introduces a novel fusion neural architecture and the use of a novel Lyapunov theory-based algorithm, for the online approximation of the dynamics of nonlinear systems. The proposed neural system, in combination with the proposed update rule of the neural weights, achieves fast convergence of the identification process, ensuring at the same time stability of the error system in the sense of Lyapunov theory. The fusion neural system combines the features that are extracted from two-independent neural streams, a feedforward and a diagonal recurrent one, satisfying different design criteria of the identification task. Simulation results for five cases reveal the approximation strength of both proposed fusion neural architecture and proposed learning algorithm. Also, additional experiments demonstrate the effectiveness in cases of parameter variations and additive noise.

scholarly journals Stochastic and vibrational resonance in complex networks of neurons

2021 ◽  
Vol 379 (2198) ◽  
Author(s):  
Ali Calim ◽  
Tugba Palabas ◽  
Muhammet Uzuntarla
Keyword(s):  
Nonlinear Systems ◽  
Complex Networks ◽  
Stochastic Resonance ◽  
Network Architecture ◽  
External Perturbation ◽  
Neural System ◽  
Neural Systems ◽  
Vibrational Resonance ◽  
Resonance Phenomena ◽  
Information Signal

The concept of resonance in nonlinear systems is crucial and traditionally refers to a specific realization of maximum response provoked by a particular external perturbation. Depending on the system and the nature of perturbation, many different resonance types have been identified in various fields of science. A prominent example is in neuroscience where it has been widely accepted that a neural system may exhibit resonances at microscopic, mesoscopic and macroscopic scales and benefit from such resonances in various tasks. In this context, the two well-known forms are stochastic and vibrational resonance phenomena which manifest that detection and propagation of a feeble information signal in neural structures can be enhanced by additional perturbations via these two resonance mechanisms. Given the importance of network architecture in proper functioning of the nervous system, we here present a review of recent studies on stochastic and vibrational resonance phenomena in neuronal media, focusing mainly on their emergence in complex networks of neurons as well as in simple network structures that represent local behaviours of neuron communities. From this perspective, we aim to provide a secure guide by including theoretical and experimental approaches that analyse in detail possible reasons and necessary conditions for the appearance of stochastic resonance and vibrational resonance in neural systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

scholarly journals Interval Type-2 Recurrent Fuzzy Neural System for Nonlinear Systems Control Using Stable Simultaneous Perturbation Stochastic Approximation Algorithm

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Ching-Hung Lee ◽  
Feng-Yu Chang
Keyword(s):  
Nonlinear Systems ◽  
Membership Function ◽  
Stochastic Approximation ◽  
Neural System ◽  
Fuzzy Membership Function ◽  
Simultaneous Perturbation Stochastic Approximation ◽  
Comparison Results ◽  
Fuzzy Neural ◽  
Interval Type

This paper proposes a new type fuzzy neural systems, denoted IT2RFNS-A (interval type-2 recurrent fuzzy neural system with asymmetric membership function), for nonlinear systems identification and control. To enhance the performance and approximation ability, the triangular asymmetric fuzzy membership function (AFMF) and TSK-type consequent part are adopted for IT2RFNS-A. The gradient information of the IT2RFNS-A is not easy to obtain due to the asymmetric membership functions and interval valued sets. The corresponding stable learning is derived by simultaneous perturbation stochastic approximation (SPSA) algorithm which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results for the chaotic system identification and the control of Chua's chaotic circuit are shown to illustrate the feasibility and effectiveness of the proposed method.

Predicting spatial activity patterns in a neural map from a probabilistic atlas of 3-D reconstructed neurons

1995 ◽  
Vol 53 ◽  
pp. 812-813
Author(s):  
G. Jacobs ◽  
F. Theunissen
Keyword(s):  
Activity Patterns ◽  
Three Dimensional ◽  
Sensory System ◽  
Neural System ◽  
Probabilistic Atlas ◽  
Uniform Sample ◽  
Dimensional Reconstruction ◽  
The Time Domain ◽  
And Function ◽  
Visualization Techniques

In order to understand how the algorithms underlying neural computation are implemented within any neural system, it is necessary to understand details of the anatomy, physiology and global organization of the neurons from which the system is constructed. Information is represented in neural systems by patterns of activity that vary in both their spatial extent and in the time domain. One of the great challenges to microscopists is to devise methods for imaging these patterns of activity and to correlate them with the underlying neuroanatomy and physiology. We have addressed this problem by using a combination of three dimensional reconstruction techniques, quantitative analysis and computer visualization techniques to build a probabilistic atlas of a neural map in an insect sensory system. The principal goal of this study was to derive a quantitative representation of the map, based on a uniform sample of afferents that was of sufficient size to allow statistically meaningful analyses of the relationships between structure and function.

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