CN117035101A - Multi-scroll attractor control method and system based on autonomous neuron - Google Patents
Multi-scroll attractor control method and system based on autonomous neuron Download PDFInfo
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Abstract
The invention relates to the technical field of neuron control, in particular to a method and a system for controlling an attractor based on autonomous neurons by multiple scrolls, wherein the method comprises the steps of constructing a three-dimensional autonomous tabu neuron model; introducing the piecewise linear saturation function into a three-dimensional autonomous tabu neuron model to obtain an IMTLN model, and generating a multi-vortex attractor by using the IMTLN model; the multi-scroll attractor is controlled by adjusting the saturation value of the piecewise linear saturation function. The three-dimensional autonomous tabu neuron model provided by the invention has the advantages of simple structure and lower realization difficulty, and can generate a multi-vortex attractor; and performing multi-scroll control through parameters and performing numerical simulation.
Description
Technical Field
The invention relates to the technical field of neuron control, in particular to a method and a system for controlling an attractor based on autonomous neurons and multiple scrolls.
Background
With the rapid development of artificial intelligence, the field of artificial neural networks is a focus of attention due to the frontier and potential application value. Researchers can use neurons to build multi-layer artificial neural networks to solve various practical problems. This approach has proven to be an effective machine learning technique and has found widespread use in the fields of computer vision, natural language processing, speech recognition, and the like.
Although many existing neuron models have been studied intensively, these common neuron models have failed to meet the increasing demands due to the continuous development and progress of technology. Therefore, new neuron models are continuously explored and developed to better adapt to various application scenes; in future artificial intelligence research, developing a class of neuron models with learning ability is one of the key scientific problems of interest to researchers.
Disclosure of Invention
Aiming at the defects of the existing algorithm, the three-dimensional autonomous tabu neuron model provided by the invention has the advantages of simple structure and lower realization difficulty, and can generate a multi-vortex attractor; and performing multi-scroll control through parameters and performing numerical simulation.
The technical scheme adopted by the invention is as follows: an autonomous neuron-based multi-scroll attractor control method and system comprise the following steps:
step one, constructing a three-dimensional autonomous tabu neuron model;
further, the formula of the three-dimensional autonomous tabu neuron model is:
where x is the neuron state, y is the tabu learning state,and->The change rate of neuron state and tabu learning state along with time is that a, b, c and d are positive control parameters, and z is the internal state of memristor; />The rate of change of the internal state of the memristor over time; k is the coupling gain.
Step two, introducing a piecewise linear saturation function into a three-dimensional autonomous tabu neuron model to obtain an IMTLN model, and generating a multi-vortex attractor by using the IMTLN model;
further, the IMTLN model has the following formula:
wherein Sat (z) =0.5 (|z+e| -z-e|), E is saturation; x is the neuron state, y is the tabu learning state,and->Is the rate of change of neuron state and tabu learning state over time; a. b, c and d are positive control parameters; z is the internal state of the memristor; />The rate of change of the internal state of the memristor over time; k is the coupling gain.
And thirdly, controlling the multi-scroll attractor by adjusting the saturation value of the piecewise linear saturation function.
Further, the saturation values include: 2.5, 4.5, 6.5, 8.5, 10.5 and 20.5.
Further, an autonomous neuron based multi-scroll attractor control system comprising: a memory for storing instructions executable by the processor; and a processor for executing instructions to implement an autonomous neuron based multi-scroll attractor control method.
Further, a computer readable medium storing computer program code which, when executed by a processor, implements an autonomous neuron based multi-scroll attractor control method.
The invention has the beneficial effects that:
1. firstly, introducing a cosine memristor function as external stimulus on the basis of a two-dimensional tabu neuron model to construct a three-dimensional autonomous tabu neuron model;
2. the scroll number of the multi-scroll chaotic attractor can be controlled by adjusting the saturation value parameter, thereby being beneficial to promoting the development of artificial intelligence and a neural network thereof.
Drawings
FIG. 1 is a block diagram of a flow chart based on autonomous neuron multi-scroll attractor control of the present invention.
FIG. 2 is a schematic diagram illustrating dynamic range control of state variables within a memristive function in accordance with the present disclosure;
fig. 3 is a numerical simulation diagram of the IMTLN model of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples, which are simplified schematic illustrations showing only the basic structure of the invention and thus showing only those constructions that are relevant to the invention.
As shown in fig. 1, the method for controlling the multi-scroll attractor based on the autonomic neurons comprises the following steps:
introducing a cosine memristor function as external stimulus on the basis of the existing two-dimensional tabu neuron model to construct a three-dimensional autonomous tabu neuron model; because the characteristic property of the function model further makes the three-dimensional autonomous tabu neuron model unstable, a piecewise linear function Sat (·) is input into a bounded cosine memristor function to replace the original cosine memristor function.
FIG. 2 is a schematic diagram illustrating the dynamic range control of state variables within a memristive function, wherein the relationship between a piecewise linear saturation function Sat (z) and a bounded cosine memristive function cos (pi Sat (z)), and the dynamic amplitude of the state variable z in the bounded cosine memristive function cos (pi Sat (z)) is controlled by the function; specifically, the scroll number can be controlled by controlling the dynamic range of the parameter adjustment state variable z; furthermore, the bounded cosine memristive function is symmetric about the origin and has a set of line balance points.
First, a two-dimensional tabu neuron model is expressed as shown in (1):
where x is the neuron state, y is the tabu learning state, a, b, c and d are all positive control parameters,and->Is the rate of change of the neuron state and the tabu learning state over time.
When an ideal magnetic control memristor is introduced, the expression is shown as (2)
Wherein,to memristive internal state, I M And V M For the current flowing on the memristor and the voltage across the memristor, W (·) is the memristive function,/->Is the internal state change rate of the memristor.
A three-dimensional autonomous tabu learning unit neuron model can be constructed, and the expression of the model is shown as (3)
Where x is the neuron state, y is the tabu learning state,and->Is the rate of change of neuron state and tabu learning state over time; a. b, c and d are positive control parameters; z is the internal state of the memristor; />The internal state change rate of memristors; k is the coupling gain.
When a piecewise linear saturation function Sat (z) is used for replacing the original z, an improved low-dimensional memristor neuron model (improved 3-D memristive tabu learning neuron), namely an IMTLN model, can be obtained, and the formula is as follows:
where Sat (z) =0.5 (|z+e| -z-e|), E is saturation, and e=2n+0.5 (N is a positive integer), thus obtaining the IMTLN model.
Fig. 3 is a numerical simulation of the IMTLN model, in which the number of scrolls is controlled by the value of E, and the values of the parameters are shown in table 1.
Table 1 values of the parameters
The specific implementation scheme is as follows:
from the piecewise linear saturation function Sat (z) versus the bounded cosine memristive function cos (pi Sat (z)) of fig. 2, it can be seen that the value of the state variable z in the bounded cosine memristive function is forced to be limited. Specifically, the saturation value E bounds the internal state z, thereby controlling the number of cycles present in the bounded cosine memristive function. The periods have a monotonically decreasing interval, so that the function curve and the transverse coordinate axis have an intersection point, and the system is easier to generate the phenomenon of multi-scroll.
Based on the scroll control scheme, the model introduces a bounded cosine memento function to replace the cosine memento function in the three-dimensional autonomous tabu neuron model, and the value of positive integer N in the piecewise linear saturation function Sat (z) is set in the model, so that the scroll number of the multi-scroll chaotic attractor generated by the three-dimensional autonomous tabu model can be effectively controlled.
When 6 representative values of n=1, 2, 3, 4, 5, 10 are selected, i.e. e=2.5, 4.5, 6.5, 8.5, 10.5, 20.5, it can be seen that the model of the present invention creates a multi-scroll chaotic attractor with 3, 5, 7, 9, 11, 21 scrolls, as shown in fig. 3, so that the control of the number of scrolls can be achieved by controlling the parameter E.
With the above-described preferred embodiments according to the present invention as an illustration, the above-described descriptions can be used by persons skilled in the relevant art to make various changes and modifications without departing from the scope of the technical idea of the present invention. The technical scope of the present invention is not limited to the description, but must be determined according to the scope of claims.
Claims (6)
1. The control method of the multi-scroll attractor based on the autonomic neuron is characterized by comprising the following steps of:
step one, constructing a three-dimensional autonomous tabu neuron model;
step two, introducing a piecewise linear saturation function into a three-dimensional autonomous tabu neuron model to obtain an IMTLN model, and generating a multi-vortex attractor by using the IMTLN model;
and thirdly, controlling the multi-scroll attractor by adjusting the saturation value of the piecewise linear saturation function.
2. The autonomous neuron based multi-scroll attractor control method of claim 1 wherein the three-dimensional autonomous tabu neuron model is formulated as:
where x is the neuron state, y is the tabu learning state,and->The change rate of neuron state and tabu learning state along with time is that a, b, c and d are positive control parameters, and z is the internal state of memristor; z is the rate of change of the internal state of the memristor over time; k is the coupling gain.
3. The autonomic neuron-based multi-scroll attractor control method of claim 1 wherein the IMTLN model has the formula:
wherein Sat (z) =0.5 (|z+e| -z-e|), E is saturation; x is the neuron state, y is the tabu learning state,andis the rate of change of neuron state and tabu learning state over time; a. b, c and d are positive control parameters; z is the internal state of the memristor; />The rate of change of the internal state of the memristor over time; k is the coupling gain.
4. The method of autonomous neuron based multi-scroll attractor control of claim 3 wherein constructing a piecewise linear saturation function having a saturation value includes: 2.5, 4.5, 6.5, 8.5, 10.5 and 20.5.
5. An autonomic neuron-based multi-scroll attractor control system comprising: a memory for storing instructions executable by the processor; a processor for executing instructions to implement the autonomous neuron based multi-scroll attractor control method of any one of claims 1-4.
6. Computer readable medium storing computer program code, characterized in that the computer program code, when executed by a processor, implements an autonomous neuron based multi-scroll attractor control method according to one of the claims 1-4.
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