Linear and Nonlinear Electrical Models of Neurons for Hopfield Neural Network

2016 ◽  
Vol 71 (11) ◽  
pp. 995-1002
Author(s):  
Farah Sarwar ◽  
Shaukat Iqbal ◽  
Muhammad Waqar Hussain
Keyword(s):  
Neural Network ◽  
Neuron Model ◽  
Deterministic Model ◽  
Hopfield Neural Network ◽  
Biological Properties ◽  
Operational Amplifiers ◽  
Nonlinear Input ◽  
Stochastic Neuron ◽  
Output Characteristics ◽  
The Stability

AbstractA novel electrical model of neuron is proposed in this presentation. The suggested neural network model has linear/nonlinear input-output characteristics. This new deterministic model has joint biological properties in excellent agreement with the earlier deterministic neuron model of Hopfield and Tank and to the stochastic neuron model of McCulloch and Pitts. It is an accurate portrayal of differential equation presented by Hopfield and Tank to mimic neurons. Operational amplifiers, resistances, capacitor, and diodes are used to design this system. The presented biological model of neurons remains to be advantageous for simulations. Impulse response is studied and conferred to certify the stability and strength of this innovative model. A simple illustration is mapped to demonstrate the exactness of the intended system. Precisely mapped illustration exhibits 100 % accurate results.

scholarly journals Chaotic Behavior Analysis of a New Incommensurate Fractional-Order Hopfield Neural Network System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Nadjette Debbouche ◽  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Giuseppe Grassi ◽  
Mohammed K. A. Kaabar ◽  
...  
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Hopfield Neural Network ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Neural Network System ◽  
The Stability ◽  
Arbitrary Location

This study intends to examine different dynamics of the chaotic incommensurate fractional-order Hopfield neural network model. The stability of the proposed incommensurate-order model is analyzed numerically by continuously varying the values of the fractional-order derivative and the values of the system parameters. It turned out that the formulated system using the Caputo differential operator exhibits many rich complex dynamics, including symmetry, bistability, and coexisting chaotic attractors. On the other hand, it has been detected that by adapting the corresponding controlled constants, such systems possess the so-called offset boosting of three variables. Besides, the resultant periodic and chaotic attractors can be scattered in several forms, including 1D line, 2D lattice, and 3D grid, and even in an arbitrary location of the phase space. Several numerical simulations are implemented, and the obtained findings are illustrated through constructing bifurcation diagrams, computing Lyapunov exponents, calculating Lyapunov dimensions, and sketching the phase portraits in 2D and 3D projections.

scholarly journals Stability Analysis of  Fractional Order Memristor Synapse-coupled Hopfield Neural Network with Ring Structure

2021 ◽  
Author(s):  
Leila Eftekhari ◽  
Mohammad Amirian
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Hopfield Neural Network ◽  
Ring Structure ◽  
Embedded Memory ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Memristor Synapse

Abstract A memristor is a non-linear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To examine the embedded memory property, we should use mathematical frameworks like fractional calculus, which is capable of doing so. Here, we first present a fractional-order memristor synapse-coupling Hopfield neural network on two neurons and then extend the model to a neural network with a ring structure that consists of $n$ sub-network neurons. Necessary and sufficient conditions for the stability of equilibrium points are investigated, highlighting the dependency of the stability on the fractional-order value and the number of neurons. Numerical simulations and bifurcation analysis, along with Lyapunov exponents, are given in the two-neuron case that substantiates the theoretical findings, suggesting possible routes towards chaos when the fractional order of the system increases. In the $n$-neuron case also, it is revealed that the stability depends on the structure and number of sub-networks.

scholarly journals Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Yaping Ren ◽  
Yongkun Li
Keyword(s):  
Neural Network ◽  
Discrete Time ◽  
Bifurcation Analysis ◽  
Hopfield Neural Network ◽  
Discrete Time System ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
The Stability ◽  
Two Parameters

A bifurcation analysis is undertaken for a discrete-time Hopfield neural network with four delays. Conditions ensuring the asymptotic stability of the null solution are obtained with respect to two parameters of the system. Using techniques developed by Kuznetsov to a discrete-time system, we study the Neimark-Sacker bifurcation (also called Hopf bifurcation for maps) of the system. The direction and the stability of the Neimark-Sacker bifurcation are investigated by applying the normal form theory and the center manifold theorem.

Enhancing the Output Characteristics of a Photovoltaic Position Sensor Using a Feed-Forward Neural Network

2009 ◽  
Vol 62-64 ◽  
pp. 506-511
Author(s):  
John T. Agee ◽  
S. Masupe ◽  
M. Jeffrey ◽  
Adisa A. Jimoh
Keyword(s):  
Neural Network ◽  
Controller Design ◽  
Position Sensor ◽  
Solar Panels ◽  
Feed Forward Neural Network ◽  
Network Training ◽  
The Neural Network ◽  
Nonlinear Input ◽  
Final Error ◽  
Output Characteristics

Tracking solar-power devices often employ photovoltaic position sensors to detect the angle of misalignment between the axis of mounted solar panels and that of sunlight. The nonlinear input-output characteristics of this type of sensors tend to complicate controller design in such systems. This paper presents a nonlinear mathematical model of the photovoltaic position sensor. A three-layer feedforward neural network was trained to linearise the characteristics of the sensor. The MATLAB neural network tool (nntool) was used for neural network training. A final error of was obtained after training. Simulation of the neural network showed that linear sensor characteristics could be reproduced throughout the domain of sensor operation.

scholarly journals Complex-Valued Associative Memories with Projection and Iterative Learning Rules

2018 ◽  
Vol 8 (3) ◽  
pp. 237-249 ◽  
Author(s):  
Teijiro Isokawa ◽  
Hiroki Yamamoto ◽  
Haruhiko Nishimura ◽  
Takayuki Yumoto ◽  
Naotake Kamiura ◽  
...  
Keyword(s):  
Neural Network ◽  
Learning Rule ◽  
Hopfield Neural Network ◽  
Iterative Learning ◽  
Associative Memories ◽  
Learning Rules ◽  
The Stability ◽  
Complex Valued ◽  
Projection Rule ◽  
Learning Schemes

AbstractIn this paper, we investigate the stability of patterns embedded as the associative memory distributed on the complex-valued Hopfield neural network, in which the neuron states are encoded by the phase values on a unit circle of complex plane. As learning schemes for embedding patterns onto the network, projection rule and iterative learning rule are formally expanded to the complex-valued case. The retrieval of patterns embedded by iterative learning rule is demonstrated and the stability for embedded patterns is quantitatively investigated.

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