CN104579629B - A kind of chaotic oscillating circuit based on titanium dioxide memristor - Google Patents
A kind of chaotic oscillating circuit based on titanium dioxide memristor Download PDFInfo
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- CN104579629B CN104579629B CN201510038029.3A CN201510038029A CN104579629B CN 104579629 B CN104579629 B CN 104579629B CN 201510038029 A CN201510038029 A CN 201510038029A CN 104579629 B CN104579629 B CN 104579629B
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Abstract
The invention discloses a kind of chaotic oscillating circuit based on titanium dioxide memristor, including RC connection in series-parallel frequency-selective networks circuit, profound and negative feedbck circuit and operational amplifier, the RC connection in series-parallel frequency-selective network circuit includes memristor, first resistor, second resistance, the first electric capacity and the second electric capacity, wherein second resistance is parallel to operational amplifier output terminal and in-phase input end after being connected with the second electric capacity, is accessed after memristor is in parallel with the first electric capacity between the in-phase input end and ground of operational amplifier；The profound and negative feedbck circuit includes 3rd resistor and the 4th resistance, and the 4th resistor coupled in parallel connects ground in the output end and inverting input of operational amplifier, the inverting input of operational amplifier by 3rd resistor.The present invention is simple in construction, and by adjusting 3rd resistor or the 4th resistance, with regard to the chaos circuit can be made to produce chaotic signal or periodic signal with different strange attractors, therefore the circuit has good application prospect in chaotic signal generation and secret communication.
Description
Technical field
The present invention relates to chaos technology field, more particularly to a kind of chaotic oscillating circuit based on titanium dioxide memristor.
Background technology
1971, scientist professor Cai Shaotang of Chinese origin proposed the concept of memristor.Memristor be considered as except resistance, electric capacity,
The 4th kind of basic circuit elements beyond inductance.Due to there is no nanometer technology also at that time, so the discovery is by stranded.Until
HP Lab exists within 2008《It is natural》An article has been delivered on magazine, has successfully confirmed the 4th kind of passive primary element ---
The presence of memristor, and successful design goes out workable memristor mock-up.The model is made of using titanium dioxide as stock
's.The appearance of memristor not only greatly enriches existing circuit component types, and supplemented with current RC, RL, LC,
The scheme of rlc circuit design, the electricity for being possible to be made up of with voltage source four primary elements of circuit can be expanded to
Road scope.Memristor has unique memory performance and circuit characteristic, therefore it is logical in fast reading and writing, frequency modulation, storage, secrecy
There is extraordinary application prospect and value in the fields such as letter, nonlinear circuit.
The content of the invention
In view of this, it is an object of the invention to provide a kind of chaotic oscillating circuit based on titanium dioxide memristor.
The purpose of the present invention is achieved through the following technical solutions, a kind of chaotic oscillation based on titanium dioxide memristor
Circuit, including RC connection in series-parallel frequency-selective networks circuit 1, profound and negative feedbck circuit 2 and operational amplifier A, the RC connection in series-parallel frequency-selecting
Lattice network 1 includes memristor M, second resistance R2, the first electric capacity C1 and the second electric capacity C2, the electricity of wherein second resistance R2 and second
Hold the output end and in-phase input end that operational amplifier A is parallel to after C2 connects, accessed after memristor M is in parallel with the first electric capacity C1
Between the in-phase input end and ground of operational amplifier；The profound and negative feedbck circuit 2 includes 3rd resistor R3 and the 4th resistance R4,
4th resistance R4 is parallel to the output end and inverting input of operational amplifier A, and the inverting input of operational amplifier passes through
Three resistance R3 connections ground.
By adopting the above-described technical solution, the present invention has the advantage that：
The circuit structure is simple, and by regulation resistance R3 or R4 resistance, has with regard to that can produce the chaos circuit
The chaotic signal or periodic signal of different strange attractors, therefore the circuit is in the generation and secret communication of chaotic signal
There is good application prospect.
Brief description of the drawings
In order that the object, technical solutions and advantages of the present invention are clearer, the present invention is made below in conjunction with accompanying drawing into
The detailed description of one step, wherein：
The physical model of Fig. 1 titanium dioxide memristors；
Fig. 2 is the circuit of the present invention；
The lyapunov index that Fig. 3 system equations change with parameter K is composed；
The single argument bifurcation graphs that Fig. 4 system equations change with parameter K；
Fig. 5 changes typical phase diagram with K；
Wherein (a) K=3.95；(b) K=4.03；(c) K=4.06；(d) K=4.08；(e) K=4.38；(f) K=4.5；
Fig. 6 circuit simulation figures,
Wherein Ron=100 Ω, Roff=10k Ω, R2=R3=10k Ω, R4=35k Ω, C1=C2=100 μ F；
The display waveform of oscillograph in Fig. 7 circuit simulation figures；
Fig. 8 circuit simulation figures；
Wherein Ron=100 Ω, Roff=10k Ω, R2=R3=10k Ω, R4=30.8k Ω, C1=C2=100 μ F；
The display waveform of oscillograph in Fig. 9 circuit simulation figures.
Embodiment
Below with reference to accompanying drawing, the preferred embodiments of the present invention are described in detail；It should be appreciated that preferred embodiment
Only for the explanation present invention, the protection domain being not intended to be limiting of the invention.
The physical model of titanium dioxide memristor as shown in Figure 1, wherein, D is the total length of titanium deoxid film, and w (t) is
The width of doped layer.Total resistance of memristor is equal to doped portion resistance and undoped partial ohmic sum as seen from the figure
Wherein RONAnd ROFFLimit memristor value during respectively w=D and w=0, w are the built-in variables of memristor.
For simplicity, we use internal state variables of the dimensionless variable z=w/D as titanium dioxide memristor,
Because of w ∈ [0, D], z ∈ [0,1] can be obtained.Make ρ=ROFF/RON, then formula (1) can turn to：
RM(z)=RONr(z)
Wherein r (z) is that dimensionless function is as follows：
R (z)=z+ ρ (1-z) (2)
Boundary Moving speed between doped layer and non-impurity-doped layer is：
Wherein, μvThe constant of ion situation of movement in uniform field is represented, i (t) is the electric current for flowing through memristor, and f (z) is mould
Intend the window function that doping face reaches memristor border ion situation of movement, f (z) function is as follows：
F (z)=1- (z-stp (- i))2
Here i ＞ 0 are worked as in stp (i)=1, and i ＜ 0 are worked as in stp (i)=0.
A kind of chaotic oscillating circuit based on titanium dioxide memristor as shown in Figure 2, including RC connection in series-parallel frequency-selective network electricity
Road 1, profound and negative feedbck circuit 2 and operational amplifier A, the RC connection in series-parallel frequency-selective network circuit 1 include memristor M, the second electricity
Resistance R2, the first electric capacity C1 and the second electric capacity C2, wherein second resistance R2 are parallel to operational amplifier A after being connected with the second electric capacity C2
Output end and in-phase input end, after memristor M is in parallel with the first electric capacity C1 access operational amplifier in-phase input end with ground
Between；The profound and negative feedbck circuit 2 includes 3rd resistor R3 and the 4th resistance R4, and the 4th resistance R4 is parallel to operational amplifier
A output end and inverting input, the inverting input of operational amplifier pass through 3rd resistor R3 connections ground.
To this chaotic oscillating circuit based on titanium dioxide memristor with Kirchoff s voltage current law and memristor
The state equation that portion's state equation (3) can obtain the circuit is as follows：
Wherein v1Represent the voltage at electric capacity C1 both ends, v2Represent the voltage at electric capacity C2 both ends, VoRepresent the defeated of operational amplifier
Go out voltage, maximum and the minimum output voltage of operational amplifier are respectively VMWith-VMIf vo=VM/ K, K=1+R4/R3, then computing
The output of amplifier is：
We do dimensionless processing to (4) formula for convenience of discussion, if
Then (4) formula can abbreviation be following formula：
Wherein h (x) is the Dimensionless Form of operational amplifier output：
With the change of (5) formula parameter, system shows extremely complex dynamic behavior, and to (5) formula, we take parameter：
ρ=100, k=1, α=β=1, K=4.5
In the phasor such as accompanying drawing 5 that are obtained by numerical simulation shown in (f), by calculating, the lyapunov index of system
For [0.061,0.000, -1.193], it is known that system is in chaos state.
Further, we have obtained situation of change of the system dynamics behavior with parameter K, and accompanying drawing 4 is changed with parameter K
The lyapunov index spectrum of system, accompanying drawing 5 is the bifurcation graphs with parameter K change systems.Accompanying drawing 4 and accompanying drawing 5 coincide very much, and two
Person illustrates that system can produce extremely complex dynamic behavior with the change of parameter.
It was found from accompanying drawing 4-5, in K ≈ 3.913, there is a periodic orbit in system.During K=3.95, typical one week
Shown in (a) of the phasor of phase track such as accompanying drawing 5；With K increase, system has led to chaos by period doubling bifurcation, in K=4.03
When, system is two cycles by a Periodic Bifurcation, shown in (b) of its phasor such as accompanying drawing 5；In K=4.06, diverge as four cycles,
Shown in (c) of its phasor such as accompanying drawing 5；Along this road, final system enters chaos state, and in K=4.08, its is typical
Shown in (d) of phasor such as accompanying drawing 5, its lyapunov index is [0.071,0.000, -4.080], it is evident that system now
In chaos state.With K change, occur some period windows in bifurcation graphs, in K=4.38, a typical week
Shown in (e) of phase orbit phase diagram such as accompanying drawing 5.After these transient behaviors, continue to increase with K, the amplitude of oscillating circuit
Slightly increase.In K=4.5, shown in (f) of its strange attractor phasor such as accompanying drawing 5, lyapunov index now is
[0.061,0.000, -1.193], it is known that system is in chaos state.
Fig. 6 is the circuit simulation figure of one of which embodiment of the present invention, and Fig. 7 is the display waveform of oscillograph in Fig. 6；Wherein
That amplifier is selected is OP262GS, and what resistance was selected is conventional, electric-resistance, and its resistance is
R2=10k Ω, R3=10k Ω, R4=(K-1) R3=35k Ω,
Titanium dioxide memristor M resistance
RON=100 Ω, ρ=ROFF/RON=100, D=10nm, uV=10-10cm2s-1V-1, vo=1V, VM=4.5V；
Electric capacity C1=C2=100 μ F.Now the systematic parameter of corresponding Non-di-mensional equation is：
K=1, α=β=1, K=4.5, wherein resistance R2With electric capacity C2Computing is parallel to after series connection to put
Big device OP262GS the first pin and the 3rd pin, titanium dioxide memristor M and electric capacity C1Operational amplifier is accessed after parallel connection
Between 3rd pin and ground, resistance R4It is parallel to the first pin and second pin of operational amplifier, the second of operational amplifier
Pin passes through resistance R3Connection ground.4th pin of operational amplifier connects -4.5V low-voltages, and the 7th pin of operational amplifier connects
4.5V high voltage.Other pins of operational amplifier are hanging.Its circuit simulation figure is as shown in Figure 7, it can be seen that itself and accompanying drawing 5
In (f) unanimously, illustrate that the circuit generates the chaotic signal with strange attractor.
Fig. 8 is the circuit simulation figure of another embodiment of the present invention；
Wherein, in Fig. 9 circuit simulations figure oscillograph display waveform, compared with Fig. 6,7, the K=4.08 in the present embodiment,
R4=30.8k Ω, wherein resistance R2With electric capacity C2The first pin that operational amplifier OP262GS is parallel to after series connection draws with the 3rd
Pin, titanium dioxide memristor M and electric capacity C1Accessed after parallel connection between the 3rd pin and ground of operational amplifier, resistance R4It is parallel to
The first pin and second pin of operational amplifier, the second pin of operational amplifier pass through resistance R3Connection ground.Operation amplifier
4th pin of device connects -4.08V low-voltages, and the 7th pin of operational amplifier connects 4.08V high voltages.Operational amplifier other
Pin is hanging.Its circuit simulation figure is as shown in Figure 9, it can be seen that it unanimously, illustrates that the circuit produces with (d) in accompanying drawing 5
There is the chaotic signal of another strange attractor.
The present invention has different strange attractors by regulation resistance R3 or R4 resistance with regard to that can produce the chaos circuit
Chaotic signal or periodic signal, therefore the circuit has good application in the generation and secret communication of chaotic signal
Prospect.
The preferred embodiments of the present invention are the foregoing is only, are not intended to limit the invention, it is clear that those skilled in the art
Member can carry out various changes and modification without departing from the spirit and scope of the present invention to the present invention.So, if the present invention
These modifications and variations belong within the scope of the claims in the present invention and its equivalent technologies, then the present invention is also intended to include these
Including change and modification.
Claims (1)
- A kind of 1. chaotic oscillating circuit based on titanium dioxide memristor, it is characterised in that：Including RC connection in series-parallel frequency-selective network circuits (1), profound and negative feedbck circuit (2) and operational amplifier (A), the RC connection in series-parallel frequency-selective network circuit (1) include memristor (M), second resistance (R2), the first electric capacity (C1) and the second electric capacity (C2), wherein second resistance (R2) are gone here and there with the second electric capacity (C2) The output end and in-phase input end of operational amplifier (A) are parallel to after connection, is accessed after memristor (M) is in parallel with the first electric capacity (C1) Between the in-phase input end and ground of operational amplifier；The profound and negative feedbck circuit (2) includes 3rd resistor (R3) and the 4th electricity Hinder (R4), the 4th resistance (R4) is parallel to the output end and inverting input of operational amplifier (A), operational amplifier it is anti-phase defeated Enter end to be grounded by 3rd resistor (R3).
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Families Citing this family (2)
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| CN105827392A (en) * | 2016-04-28 | 2016-08-03 | 李博雅 | Simplest series memristor circuit |
| CN107122555A (en) * | 2017-05-03 | 2017-09-01 | 湖北科技学院 | A kind of equivalent simulation circuit of Hewlett-Packard's memristor model |
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|---|---|---|---|---|
| CN102570976A (en) * | 2011-12-20 | 2012-07-11 | 华中科技大学 | Memristor-based Van der pol oscillator circuit |
| CN103023434A (en) * | 2013-01-09 | 2013-04-03 | 武汉科技大学 | Memristor based frequency-adjustable sine wave oscillating circuit |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| WO2011099961A1 (en) * | 2010-02-09 | 2011-08-18 | Hewlett-Packard Development Company, L.P. | Memory resistor adjustment using feedback control |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102570976A (en) * | 2011-12-20 | 2012-07-11 | 华中科技大学 | Memristor-based Van der pol oscillator circuit |
| CN103023434A (en) * | 2013-01-09 | 2013-04-03 | 武汉科技大学 | Memristor based frequency-adjustable sine wave oscillating circuit |
Non-Patent Citations (3)
| Title |
|---|
| A Simpler Modified Wien-bridge Oscillator for ‘2D’Chaos;Qingdu Li 等;《IEEE》;20050815;第1159-1161页 * |
| Memristor Based Feedback Systems;Milan Stork 等;《IEEE》;20091110;全文 * |
| 基于Chua电路的四维超混沌忆阻电路;杨芳艳 等;《物理学报》;20140423;全文 * |
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