STOCHASTIC RESONANCE IN HINDMARSH–ROSE NEURAL NETWORK WITH SMALL-WORLD CONNECTIONS

We study stochastic resonance (SR) in Hindmarsh–Rose (HR) neural network with small-world (SW) connections driven by external periodic stimulus, focusing on the dependence of properties of SR on the network structure parameters. It is found that, the SW neural network enhances SR compared with single neuron. By turning coupling strength c, two categories of SR were gained. With the connection-rewiring probability p increasing, the resonance curve becomes more and more sharp and the peak value increases gradually and then reaches saturation. The SW network enhances the SR peak value compared with regular network and widens resonance in ascending range compared with random network. When decreasing node degree k, the resonance range is enlarged, and the signal noise ratio (SNR) curve becomes a two peak one from a classic single peak SR curve, and then the stochastic resonance phenomenon almost disappears.

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A New Small-World Neural Network with its Performance on Fault Tolerance

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.629.719 ◽

2012 ◽

Vol 629 ◽

pp. 719-724

Author(s):

Xiao Hu Li ◽

Feng Xu ◽

Jin Hua Zhang ◽

Su Nan Wang

Keyword(s):

Neural Network ◽

Neural Networks ◽

Fault Tolerance ◽

Random Network ◽

Small World ◽

Simple Simulation ◽

Neuron Damage ◽

Regular Network ◽

Artificial Neural ◽

And Function

Many artificial neural networks are the simple simulation of brain neural network’s architecture and function. However, how to rebuild new artificial neural network which architecture is similar to biological neural networks is worth studying. In this study, a new multilayer feedforward small-world neural network is presented using the results form research on complex network. Firstly, a new multilayer feedforward small-world neural network which relies on the rewiring probability heavily is built up on the basis of the construction ideology of Watts-Strogatz networks model and community structure. Secondly, fault tolerance is employed in investigating the performances of new small-world neural network. When the network with connection fault or neuron damage is used to test the fault tolerance performance under different rewiring probability, simulation results show that the fault tolerance capability of small-world neural network outmatches that of the same scale regular network when the fault probability is more than 40%, while random network has the best fault tolerance capability.

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On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2020.0229 ◽

2021 ◽

Vol 379 (2192) ◽

pp. 20200229 ◽

Cited By ~ 3

Author(s):

V. Sorokin ◽

I. Demidov

Keyword(s):

Stochastic Resonance ◽

High Frequency ◽

Stochastic Systems ◽

Signal To Noise Ratio ◽

Nonlinear Damping ◽

Resonance Phenomenon ◽

Oscillatory Systems ◽

Stochastic Excitations ◽

Viable Approach ◽

Stochastic Resonance Phenomenon

Adding noise to a system can ‘improve’ its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this ‘deterministic’ approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

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Verification of the analysis technique of a minute vibration waveform using a stochastic resonance phenomenon

The Proceedings of the Symposium on Evaluation and Diagnosis ◽

10.1299/jsmesed.2017.16.105 ◽

2017 ◽

Vol 2017.16 (0) ◽

pp. 105

Author(s):

Yuya Nishi

Keyword(s):

Stochastic Resonance ◽

Resonance Phenomenon ◽

Analysis Technique ◽

Stochastic Resonance Phenomenon

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MICROSCOPIC SELF-ORGANIZATION IN NETWORKS AND REGULAR LATTICE

Modern Physics Letters B ◽

10.1142/s0217984902004391 ◽

2002 ◽

Vol 16 (25) ◽

pp. 923-935

Author(s):

QI OUYANG ◽

KAI SUN ◽

HONGLI WANG

Keyword(s):

Correlation Length ◽

Random Network ◽

Reaction System ◽

Small World ◽

Self Organization ◽

Fast Diffusion ◽

Small World Network ◽

Regular Lattice ◽

Numerical Studies ◽

Regular Network

We report our numerical studies on the microscopic self-organizations of a reaction system in three types of networks: a regular network, a small-world network, and a random network as well as on a regular lattice. Our simulation results show that the topology of the network has an important effect on the communication among reaction molecules, and plays an important role in microscopic self-organization. The correlation length among reacting molecules in a random or a small-world network is much shorter compared with that in the regular network. As a result, it is much easier to obtain a microscopic self-organization in a small-world or a random network. A phase transition from a stochastic state to a synchronized state was observed when the randomness of a small-world network was increased. We also demonstrate that good synchronization activities of enzymatic turnover cycles can be developed on a regular lattice when the correlation length created by the fast diffusion of regulatory particles is large enough.

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Synchronization and stochastic resonance of the small-world neural network based on the CPG

Cognitive Neurodynamics ◽

10.1007/s11571-013-9275-8 ◽

2013 ◽

Vol 8 (3) ◽

pp. 217-226 ◽

Cited By ~ 15

Author(s):

Qiang Lu ◽

Juan Tian

Keyword(s):

Neural Network ◽

Stochastic Resonance ◽

Small World

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On the stochastic resonance phenomenon in parametrically excited systems

European Journal of Applied Mathematics ◽

10.1017/s0956792518000608 ◽

2018 ◽

Vol 30 (5) ◽

pp. 986-1003 ◽

Cited By ~ 3

Author(s):

VLADISLAV SOROKIN ◽

ILIYA BLEKHMAN

Keyword(s):

Stochastic Resonance ◽

High Frequency ◽

Stochastic Systems ◽

Resonance Phenomenon ◽

Deterministic Approach ◽

Parametrically Excited ◽

System Behaviour ◽

Input Signals ◽

Mass Properties ◽

Stochastic Resonance Phenomenon

The stochastic resonance phenomenon implies “positive” changing of a system behaviour when noise is added to the system. The phenomenon has found numerous applications in physics, neuroscience, biology, medicine, mechanics and other fields. The present paper concerns this phenomenon for parametrically excited stochastic systems, i.e. systems that feature deterministic input signals that affect their parameters, e.g. stiffness, damping or mass properties. Parametrically excited systems are now widely used for signal sensing, filtering and amplification, particularly in micro- and nanoscale applications. And noise and uncertainty can be essential for systems at this scale. Thus, these systems potentially can exhibit stochastic resonance. In the present paper, we use a “deterministic” approach to describe the stochastic resonance phenomenon that implies replacing noise by deterministic high-frequency excitations. By means of the approach, we show that stochastic resonance can occur for parametrically excited systems and determine the corresponding resonance conditions.

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Investigation of a Nonlinear Vibrational Energy Harvester in the Stochastic Resonance Regime

Proceedings ◽

10.3390/proceedings2131092 ◽

2018 ◽

Vol 2 (13) ◽

pp. 1092 ◽

Cited By ~ 1

Author(s):

Bruno Andò ◽

Salvatore Baglio ◽

Adi R. Bulsara ◽

Vincenzo Marletta

Keyword(s):

Stochastic Resonance ◽

Energy Harvester ◽

Vibrational Energy ◽

Wide Band ◽

Resonance Phenomenon ◽

Sinusoidal Vibration ◽

Sinusoidal Input ◽

Optimal Value ◽

Stochastic Resonance Phenomenon ◽

Nonlinear Energy

In this paper the possibility to exploit advantageously the Stochastic Resonance phenomenon in a Nonlinear Energy Harvester to scavenge energy from wide band mechanical vibrations is experimentally demonstrated. The device is demonstrated to be capable of scavenging energy in case of a subthreshold sinusoidal vibration and a wideband noise (limited at 100 Hz) superimposed. The existence of an optimal value of the noise intensity maximizing the switching ratio of the bistable beam, then the performances, is experimentally demonstrated. The harvester is observed to generate power up to about 60 µW and 150 µW in case of a subthreshold sinusoidal input at 1 Hz and 3 Hz with a superimposed noise limited at 100 Hz.

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