CN110956250A

CN110956250A - Double-memristor Hopfield neural network model with coexisting multiple attractors

Info

Publication number: CN110956250A
Application number: CN201811127495.9A
Authority: CN
Inventors: 钱辉; 武洲; 姚肖勇; 杨艳
Original assignee: Changzhou Xingyu Automotive Lighting Systems Co Ltd
Current assignee: Changzhou Xingyu Automotive Lighting Systems Co Ltd
Priority date: 2018-09-27
Filing date: 2018-09-27
Publication date: 2020-04-03

Abstract

The invention discloses a double-memristor Hopfield neural network model with coexisting multiple attractors, and relates to the field of application of Hopfield neural network models. The invention introduces two memristors in a three-neuron Hopfield neural network to respectively replace two resistive coupling quantities in an original coupling weight matrix. By changing the initial value of the state variable in the model, different types of multi-attractor coexistence phenomena can be shown under different internal parameters of the memristor, so that complex dynamic behaviors in the brain are simulated.

Description

Double-memristor Hopfield neural network model with coexisting multiple attractors

Technical Field

The invention relates to the application field of Hopfield neural network models, in particular to a double-memristor Hopfield neural network model with coexisting multiple attractors.

Background

It is known that human beings have much better abilities of movement, cognition, learning, etc. than other mammals, and the formation of these abilities depends mainly on the cooperative cooperation among neurons in the complex neural network system in the human body. From the beginning of the last century, people construct various artificial neural network models which can meet different requirements of people on the basis of the research on the biological neural network, and continuously improve and perfect the artificial neural network models. Among the numerous neural network models, the Hopfield neural network proposed by professor john Hopfield is an important milestone in the development history of neural networks.

The Hopfield neural network model is a feedback type neural network, and has the most important characteristic that the Hopfield neural network model has an associative memory function and can copy the functions of the human brain. In recent years, more and more evidences show that complex chaotic dynamics exist in the brain, and the Hopfield neural network can better simulate chaotic behaviors in the brain and is an important model for artificial neural computation. The Hopfield neural network model embodies the coupling connection weight of synapses between neurons and has good reference function for deeply researching and simulating brain functions of people.

The concept of the memristor is firstly proposed by professor Chuai begonia, and the memristor is a nonlinear resistor with a memory function. Research shows that memristors are the best way for realizing artificial neural network synapses by hardware, which can be found by people so far. A Hopfield neural network model based on memristions is constructed by using the memristions, and the coexistence behavior of multiple attractors is found in the new model. The multi-stability research is beneficial to further understanding the practical application value of the Hopfield neural network in associative memory and pattern recognition.

Disclosure of Invention

In view of the above situation, the present invention provides a dual memristive Hopfield neural network model with coexisting multiple attractors.

In order to achieve the purpose, the invention adopts the following technical scheme:

a double-memristor Hopfield neural network model with coexisting multiple attractors is constructed by introducing two memristors into a three-neuron Hopfield neural network, respectively replacing two resistive coupling quantities in an original coupling weight matrix and simulating biological synapses by using the memristors; by changing the initial value of the state variable in the model, different types of multi-attractor coexistence phenomena are shown under different internal parameters of the memristor, so that complex dynamic behaviors in the brain are simulated.

Further, the double-memristive Hopfield neural network model comprises a three-neuron memristive Hopfield neural network model and two non-ideal hyperbolic memristive models.

Has the advantages that:

the method comprises the steps of replacing two coupling weights in a synapse weight matrix of a three-neuron Hopfield neural network with memristive coupling weights respectively, simulating biological synapses by using memristors, and constructing a double-memristive Hopfield neural network model capable of generating coexistence of multiple attractors, wherein the model is used for simulating complex and rich dynamic behaviors in the biological neural network and revealing a complex and singular phenomenon of multi-stability.

Drawings

FIG. 1 is a connection topology diagram of a dual memristive Hopfield neural network model with co-existing multiple attractors, in accordance with the present invention;

FIG. 2(a) is a memristor W of the present invention₂Internal parameter b of 0.2, memristor W₁With the internal parameter a of the state variable x₁A bifurcation graph of the changes;

FIG. 2(b) is a memristor W of the present invention₁Internal parameter a of 0.1, memristor W₂With the internal parameter b of the state variable x₁A bifurcation graph of the changes;

FIG. 3(a) is a memristor W of the present invention₂Internal parameter b of 0.2, memristor W₁When the internal parameter a is-0.1835, x₁-x₃Phase rail diagram on the plane;

FIG. 3(b) is a memristor W of the present invention₂Internal parameter b of 0.2, memristor W₁When the internal parameter a of (2) is 0.15, x₁-x₃Phase rail diagram on the plane;

FIG. 4(a) is a memristor W of the present invention₁Internal parameter a of 0.1, memristor W₂When the internal parameter b is-0.15, x₁-x₃Phase rail diagram on the plane;

FIG. 4(b) is a memristor W of the present invention₁Internal parameter a of 0.1, memristor W₂When the internal parameter b of (2) is 0.2, x₁-x₃Phase diagram on a plane.

Detailed Description

The invention is further illustrated with reference to the following figures and examples.

The invention provides a double-memristor Hopfield neural network model with coexisting multiple attractors, which is connected in a topology as follows:

the structure includes: three neurons and two memristors, as shown in fig. 1.

In the first neuron, the self-coupling connection weight of the first neuron is-1.4; the coupling connection weight of the second neuron to the first neuron is 1.2; the coupling connection weight of the third neuron to the first neuron is-7.

In the second neuron, the second neuron is not self-coupled; the coupling weight of the first neuron to the second neuron is k₁W₁Wherein W is₁To memory resistance, k₁Is the coupling strength; the coupling connection weight of the third neuron to the second neuron is 2.8.

In the third neuron, the self-coupling connection weight of the third neuron is 4; the coupling connection weight of the first neuron to the third neuron is 0.8; the coupling weight of the second neuron to the third neuron is-k₂W₂Wherein W is₂To memory resistance, k₂Is the coupling strength.

Both the memristors are non-ideal memristors based on hyperbolic functions.

The Hopfield Neural Network (HNN) may be characterized by a set of circuit state equations for n neurons. For the ith neuron, the circuit state equation is expressed as:

wherein x is_iTo represent a capacitance C_iState variable of the voltage across R_iTo represent the resistance of the membrane resistance between the inside and outside of the neuron, I_iFor input of bias current, tanh (x)_j) Is a neuron activation function representing an input from a j-th neuron, and W ═ W_ij) Is an n x n synaptic weight matrix representing the strength of the connection between the ith and jth neurons.

In the HNN model, the neuron activation function is a monotonic differentiable function with an upper bound and a lower bound. Therefore, a hyperbolic tangent function is generally used as a neuron activation function. When the hyperbolic non-ideal memristor represented by the following formula (2) replaces the resistive coupling amount of the connection, a memristor-based HNN can be easily constructed.

Wherein W (Φ) ═ 1-atanh (Φ). Only HNNs containing three neurons are considered in this example.

Corresponding to the connection topology shown in fig. 1, the connection matrix considered has the following form:

suppose n is 3, C_i＝1、R_i＝1、I _i0 and RC 1. An autonomous ordinary differential equation in a dimensionless form describing the memristive network may be derived as:

wherein k represents the coupling strength of the hyperbolic memristor, and a and b are memristors W₁And memory resistance W₂The parameters k, a, b are all constants. Therefore, a dual memristive HNN with co-existing multiple attractors can be modeled by equation (4) above, which is a five-dimensional autonomous non-linear dynamical system.

Numerical simulation: selecting initial conditions of 5 state variables as (0, 10-9, 0, 0, 0), (0, 10-9, 0.1, 0, 0) and (0, 10-9, 0.2, 0, 0), and setting coupling strength k₁＝1、k ₂2, and respectively store the memristor W₂Is set to 0.2, in the region [ -0.2, 0.3]Internal regulation memristor W₁And internal parameter a of, and memristor W₁Is set to 0.1, in the region [ -0.2, 0.3 [ - ]]Internal regulation memristor W₂The internal parameter b of (a) can reveal the coexistence behavior of multiple attractors of the double-memristive HNN through bifurcation and phase-track diagrams.

When memory resistance W₂Is set to 0.2, in the region [ -0.2, 0.3]Internal regulation memristor W₁With the state variable x₁The branch diagram of (A) is shown in FIG. 2, and the memory resistance W is taken₁When the internal parameter a is-0.1835, at x₁-x₃There are three different types of attractor coexistence behaviors on the plane, as shown in fig. 3 (a); memory resistance W₁When the internal parameter a of (2) is 0.15, x is₁-x₃The coexistence behavior of the chaotic attractors and the cycle-limit loop exists on the plane, as shown in fig. 3 (b);

when memory resistance W₁Is set to 0.1, in the region [ -0.2, 0.3 [ - ]]Internal regulation memristor W₂Internal parameter b, dependent on the state variable x₁The branch diagram of (A) is as shown in FIG. 2(b), and the memristor W is taken₂When the internal parameter b is-0.15, at x₁-x₃The coexistence behavior of periodic attractors with two different periods on the plane is shown in fig. 4 (a); memory resistance W₂0.2 in x₁-x₃The coexistence behavior of the chaotic attractors and the periodic two-limit loop exists on the plane, as shown in fig. 4 (b).

Therefore, the invention constructs a double-memristor Hopfield neural network model with coexisting multiple attractors.

The limitation of the protection scope of the present invention is understood by those skilled in the art, and various modifications or changes which can be made by those skilled in the art without inventive efforts based on the technical solution of the present invention are still within the protection scope of the present invention.

Claims

1. A double-memristor Hopfield neural network model with coexisting multiple attractors is characterized in that: the double-memristor Hopfield neural network model is constructed by introducing two memristors into a three-neuron Hopfield neural network and simulating biological synapses by using the memristors; by changing the initial value of the state variable in the model, different types of multi-attractor coexistence phenomena are shown under different internal parameters of the memristor, so that complex dynamic behaviors in the brain are simulated.

2. The dual memristive Hopfield neural network model with co-existing multi-attractors, as in claim 1, wherein: the double-memristor Hopfield neural network model comprises a three-neuron memristor Hopfield neural network model and two non-ideal hyperbolic memristor models.