CN109347616A - A kind of chaos circuit based on fractional order memristor - Google Patents
A kind of chaos circuit based on fractional order memristor Download PDFInfo
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Abstract
The invention discloses a kind of chaos circuits based on fractional order memristor, the fractional order capacitor including being sequentially connected and being formed closed circuitFractional order capacitorResistance R, the fractional order capacitorBoth ends be parallel with fractional order inductance Lλ, the fractional order capacitorBoth ends be parallel with negative resistance G, the both ends of the negative resistance G are also parallel with fractional order memristor Mλ；By can more accurately simulate true broad sense memristor with the circuit, play an important role to analysis chaotic systems with fractional order, especially fractional order memristor chaos system；The chaos system can carry out numerical simulation and circuit simulation, it can produce Double Scroll and single scrollwork attractor according to adjustment parameter, become a kind of simple Chua's chaotic circuit, the new phenomenon that there is the dynamic behavior of fractional order memristor chaos circuit of the invention integer rank not have has researching value abundant.
Description
Technical field
The invention belongs to chaos system signal generator design fields, and in particular to one kind is based on fractional order memristor
The chaos circuit of device.
Background technique
Memristor is a kind of circuit devcie for indicating magnetic flux and charge relationship, has the dimension of resistance, but different with resistance
, the resistance value of memristor is determined by the charge for flowing through it, plays the role of remembering charge.2008, the research people of Hewlett-Packard
Member makes a nanometer memory resistor for the first time, starts memristor research boom.The appearance of nanometer memory resistor, is expected to realize non-volatile
Random access memory.Also, the integrated level of the random access memory based on memristor, power consumption, read or write speed will be more random than traditional
Memory is superior.In addition, memristor is the best way of hardware realization artificial neural network cynapse.Due to the non-linear property of memristor
Matter can produce chaos circuit, to also there is many applications in secret communication.
The scholars such as Corinto in 2012 have been put forward for the first time the second order broad sense memristor based on diode bridge and rlc circuit,
And in 2014, packet Bocheng professor team demonstrates diode-bridge circuit series connection single order RL circuit and equally meets the three of memristor
A substantive characteristics, therefore can be described as broad sense memristor, it may be constructed chaos circuit.
Fractional calculus can preferably reflect and describe actual object as the extension of integer rank calculus.
By the way that model is generalized to fractional order, available new fractional model obtains richer dynamic behavior and chaos row
For.
Summary of the invention
The object of the present invention is to provide a kind of chaos circuits based on fractional order memristor, and providing one kind can carry out
The fractional order memristor chaos circuit of numerical simulation and circuit simulation.
The technical scheme adopted by the invention is that a kind of chaos circuit based on fractional order memristor, including be sequentially connected
And form the fractional order capacitor of closed circuitFractional order capacitorResistance R, fractional order capacitorBoth ends be parallel with point
Number rank inductance Lλ, fractional order capacitorBoth ends be parallel with negative resistance G, the both ends of negative resistance G are also parallel with fractional order memristor Mλ。
The features of the present invention also characterized in that:
Fractional order memristor MλIncluding diode-bridge circuit, diode-bridge circuit both ends are also parallel with RL filter.
Diode-bridge circuit includes the concatenated diode VD of positive and negative terminal1, diode VD2Concatenated two pole of positive and negative terminal and
Pipe VD3, diode VD4, the diode VD1Negative terminal and diode VD3Negative terminal connection, diode VD2Anode and two poles
Pipe VD4Anode connection.
RL filter includes the resistance R being cascadedmWith fractional order inductanceResistance RmWith the diode VD4's
Anode connection, fractional order inductanceWith the diode VD3Negative terminal connection.
Fractional order inductanceWith fractional order inductance LλIt include a resistance Rin, resistance RinMultiple equivalent electricity of RL in parallel
Road, each RL equivalent circuit include the resistance R being cascadednWith inductance Ln。
Negative resistance G includes adder, by resistance R between adder anode and output enda1Connection, adder negative terminal and output
By resistance R between enda2The negative terminal of connection, adder connects a resistance Rb。
Fractional order capacitorFractional order capacitorIt include a resistance Rin, resistance RinIt connects the equivalent electricity of multiple RC
Road, each RC equivalent circuit include the capacitor C being connected in parallelnWith resistance Rn。
The beneficial effects of the present invention are:
A kind of chaos circuit based on fractional order memristor of the present invention, by using the circuit can more accurate mould
Intend true broad sense memristor, plays an important role to analysis chaotic systems with fractional order, especially fractional order memristor chaos system；
The chaos system can carry out numerical simulation and circuit simulation, can produce Double Scroll and single scrollwork according to adjustment parameter
Attractor becomes a kind of simple Chua's chaotic circuit, has very big impetus for the development of chaos system.
Detailed description of the invention
Fig. 1 is a kind of circuit diagram of the chaos circuit based on fractional order memristor of the present invention；
Fig. 2 is diode-bridge circuit series connection single order RL in a kind of chaos circuit based on fractional order memristor of the present invention
The broad sense memristor circuit that circuit is constituted；
Fig. 3 is a kind of chaos circuit mid-score rank induction equivalent circuit based on fractional order memristor of the present invention；
Fig. 4 is a kind of chaos circuit mid-score rank capacitor equivalent circuit based on fractional order memristor of the present invention；
Fig. 5 is negative resistance equivalent circuit in a kind of chaos circuit based on fractional order memristor of the present invention；
Fig. 6 (a) is a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention when being 0.98 rank
v2-v1Phasor；
Fig. 6 (b) is a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention when being 0.98 rank
v2-i3Phasor；
Fig. 6 (c) is a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention when being 0.98 rank
v2-iLPhasor；
Fig. 6 (d) is a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention when being 0.98 rank
v2-imPhasor；
Fig. 7 is a kind of chaos circuit mid-score rank memristor chaos system based on fractional order memristor of the present invention with order λ
The bifurcation graphs of variation；
Fig. 8 (a) be a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention be 0.955 rank and
V when 0.965 rank2-v1Compare phasor；
Fig. 8 (b) be a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention be 0.955 rank and
V when 0.965 rank1-i3Compare phasor；
Fig. 9 is that a kind of chaos circuit mid-score rank memristor chaos system order based on fractional order memristor of the present invention is
When 0.92 rank and 1 rank with fractional order inductance LλThe bifurcation graphs of variation；
Figure 10 is that a kind of chaos circuit mid-score rank memristor chaos based on fractional order memristor of the present invention realizes circuit
Figure；
Figure 11 (a) is a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention when being 0.98 rank
V2-v1Phase PSpice circuit simulation figure；
Figure 11 (b) is a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention when being 0.98 rank
V2-i3Phase PSpice circuit simulation figure；
Figure 11 (c) is a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention when being 0.98 rank
V2-iLPhase PSpice circuit simulation figure；
Figure 11 (d) is a kind of chaos circuit mid-score rank order based on fractional order memristor of the present invention when being 0.98 rank
V2-imPhase PSpice circuit simulation figure.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
A kind of chaos circuit based on fractional order memristor of the present invention, as shown in Figure 1, including being sequentially connected and being formed to close
Close the fractional order capacitor in circuitFractional order capacitorResistance R, fractional order capacitorBoth ends be parallel with fractional order inductance
Lλ, fractional order capacitorBoth ends be parallel with negative resistance G, the both ends of negative resistance G are also parallel with fractional order memristor Mλ。
As shown in Fig. 2, fractional order memristor MλIncluding diode-bridge circuit, diode-bridge circuit both ends are also in parallel
There is RL filter；Diode-bridge circuit includes the concatenated diode VD of positive and negative terminal1, diode VD2And positive and negative terminal concatenated two
Pole pipe VD3, diode VD4, diode VD1Negative terminal and diode VD3Negative terminal connection, diode VD2Anode and diode
VD4Anode connection；RL filter includes the resistance R being cascadedmWith fractional order inductanceResistance RmWith two pole
Pipe VD4Anode connection, fractional order inductanceWith diode VD3Negative terminal connection.
As shown in figure 3, fractional order inductanceWith fractional order inductance LλIt include a resistance Rin, resistance RinIt is in parallel multiple
RL equivalent circuit, each RL equivalent circuit include the resistance R being cascadednWith inductance Ln。
As shown in figure 4, fractional order capacitorFractional order capacitorIt include a resistance Rin, resistance RinIt connects multiple
RC equivalent circuit, each RC equivalent circuit include the capacitor C being connected in parallelnWith resistance Rn。
As shown in figure 5, negative resistance G includes adder, by resistance R between the adder anode and output enda1Connection, institute
It states between adder negative terminal and output end by resistance Ra2The negative terminal of connection, the adder connects a resistance Rb。
Mathematical model in existing broad sense memristor can be indicated by following equation:
im=(2IS+iL)tanh(ρum) (1)
Wherein ρ=1/ (2nVT), IS、n、VTRespectively indicate diode reverse saturation current, emission ratio and thermal voltage.Separately
Outside, iLRepresent the electric current for flowing through inductance L, umRepresent input voltage and imIndicate the input current of broad sense memristor.By formula (1) two
End is the same as except um, can obtain the broad sense memristor is voltage-controlled memristor, and memristor value can be expressed from the next:
Above-mentioned model is generalized to fractional order, can goals for rank broad sense memristor mathematical model it is as follows:
The mathematical model for the chaos system that fractional order broad sense memristor of the present invention is realized can be by four state variables
It indicates, respectively fractional order capacitorThe voltage v at both ends1, fractional order capacitorThe voltage v at both ends2, flow through fractional order inductance
LλElectric current i3With fraction reacted rank memristor MλInternal state variable flows through fractional order inductanceElectric current iL.By right
Circuit shown in FIG. 1 uses Kirchhoff's second law and Kirchhoff's current law (KCL), can obtain the mathematical modulo of this chaos system
Type is expressed from the next:
Numerical simulation:
In order to verify the above-mentioned chaos system realized based on fractional order broad sense memristor, counted using MATLAB software
Value emulation, mathematical model are provided by formula (5).By using predictor-corrector method to formula (5), relevant parameter is chosen as follows: IS=
2.682nA, ρ=10.89,Lλ=12mH, R=2k Ω, G=0.6667mS,Rm=580 Ω, fractional order order are chosen to be λ=0.98, and the initial value of four state variables is set as v1=
0V,v2=0.01V, i3=0A, iL=0A, can goals for rank order be 0.98 rank when v2-v1Phasor, as shown in Fig. 6 (a).Figure
In can clearly find out, the system in 0.98 rank be in chaos state.Fig. 6 (b) and Fig. 6 (c) is respectively fractional order rank
Secondary v when being 0.98 rank2-i3And v2-iLPhasor.Fig. 6 (d) show v when fractional order order is 0.98 rank2-imPhasor, i.e.,
The foreign current voltage characteristic of above-mentioned fractional order broad sense memristor, it is seen that its external characteristics is the hysteresis loop tightened in origin, and
And meet three features of memristor, therefore also demonstrate the feasibility of this fractional order broad sense memristor.
In order to analyze influence of the order to fractional order memristor chaos circuit, fractional order memristor state of chaotic system variable v1
(t) bifurcation graphs changed with order λ are as shown in Figure 7.As seen from the figure, the dynamic behavior of system can be divided into three kinds of states: period
State, fork and chaos.As seen from Figure 7, there are two chaotic regions when order changes to 1 from 0.9 for the system.With rank
The increase of secondary λ, system enter chaos state from periodic state suddenly.However, there are the times not to grow for chaotic behavior, when order is rigid
When greater than 0.94 rank, system is returned to period state.When order is higher than 0.97 rank, system is again introduced into chaos.In addition, working as rank
Secondary when being greater than 0.96 rank, system shows complicated Nonlinear dynamic behaviors, such as fork and chaos.In order to further illustrate
Influence of the order to system dynamics behavior, Fig. 8 (a), 8 (b) give fractional order of the order equal to 0.955 and 0.965 when
The comparison phasor of memristor chaos circuit.As can be seen that different orders can make system generate different dynamic behaviors, make be
System is in monocycle or multiple periods.Fig. 9 gives shape of the fractional order memristor chaos system when order is 0.92 rank and 1 rank
State variable v1(t) with fractional order inductance LλThe bifurcation graphs of variation, equally it is also seen that different orders can be to the power of system
Scholarship and moral conduct is to generate different influences.
Circuit simulation:
In order to further verify the feasibility of proposed fractional order memristor chaos system, the present invention is soft using PSpice
Part carries out circuit simulation, and the realization circuit diagram for the fractional order memristor chaos system invented is as shown in Figure 10.Fractional order inductance
Parallel equivalent circuit is as shown in Figure 3.The transmission function of fractional order inductance can indicate are as follows:
By solution formula (6), can obtain:
Similarly, the transmission function of fractional order capacitor can indicate are as follows:
By solution formula (8), can obtain:
When order is chosen to be 0.98 rank, inductanceCapacitorCapacitorInductance Lλ=12mH, n=7, can be in the hope of fractional order equivalent capacity, equivalent electricity according to formula (7) and formula (9)
The parameter of sense and resistance.Design parameter is shown in Table shown in 1- table 4.
The equivalent inductance calculated value of 1 inductance of table
The equivalent resistance calculated value of 2 inductance of table
The equivalent capacity calculated value of 3 capacitor of table
The equivalent resistance calculated value of 4 capacitor of table
Be utilized respectively table parameter designing order be 0.98 rank when memristor chaos circuit and carry out circuit simulation, test
Result figure is as shown in figure 11.It can be seen that system is in chaos state, the knot of this result and numerical simulation when order is 0.98 rank
Fruit is completely the same, demonstrates the correctness of theory analysis.
By the above-mentioned means, a kind of fractional-order chaos circuit circuit based on fractional order memristor of the present invention, using simple
Traditional cai's circuit, and Cai Shi diode is replaced by fractional order memristor, which is cascaded by diode bridge
Single order parallel connection RL filter realizes, wherein inductance in fractional order memristorCapacitor in chaos circuitInductance Lλ
All it is fractional order, is made of corresponding equivalent circuit, to realizes a kind of fractional order chaos electricity based on fractional order memristor
Road, the no ground limitation of fractional order memristor, and due to reality being more in line with, to theoretical research and full-scale investigation for fractional order
It is all of great significance, memristor circuit structure is simple, is easy to circuit realization.
Claims (7)
1. a kind of chaos circuit based on fractional order memristor, which is characterized in that including being sequentially connected and forming closed circuit
Fractional order capacitorFractional order capacitorResistance R, the fractional order capacitorBoth ends be parallel with fractional order inductance Lλ, institute
State fractional order capacitorBoth ends be parallel with negative resistance G, the both ends of the negative resistance G are also parallel with fractional order memristor Mλ。
2. a kind of chaos circuit based on fractional order memristor according to claim 1, which is characterized in that the fractional order
Memristor MλIncluding diode-bridge circuit, the diode-bridge circuit both ends are also parallel with RL filter.
3. a kind of chaos circuit based on fractional order memristor according to claim 2, which is characterized in that the diode
Bridge circuit includes the concatenated diode VD of positive and negative terminal1, diode VD2And the concatenated diode VD of positive and negative terminal3, diode VD4,
The diode VD1Negative terminal and the diode VD3Negative terminal connection, the diode VD2Anode and the diode
VD4Anode connection.
4. a kind of chaos circuit based on fractional order memristor according to claim 3, which is characterized in that the RL filtering
Device includes the resistance R being cascadedmWith fractional order inductanceThe resistance RmWith the diode VD4Anode connection, institute
State fractional order inductanceWith the diode VD3Negative terminal connection.
5. a kind of chaos circuit based on fractional order memristor according to claim 4, which is characterized in that the fractional order
InductanceWith the fractional order inductance LλIt include a resistance Rin, the resistance RinMultiple RL equivalent circuits in parallel, Mei Gesuo
Stating RL equivalent circuit includes the resistance R being cascadednWith inductance Ln。
6. a kind of chaos circuit based on fractional order memristor according to claim 1, which is characterized in that the negative resistance G
Including adder, by resistance R between the adder anode and output enda1Connection, between the adder negative terminal and output end
By resistance Ra2The negative terminal of connection, the adder connects a resistance Rb。
7. a kind of chaos circuit based on fractional order memristor according to claim 1, which is characterized in that the fractional order
CapacitorFractional order capacitorIt include a resistance Rin, the resistance RinIt connects multiple RC equivalent circuits, each RC
Equivalent circuit includes the capacitor C being connected in parallelnWith resistance Rn。
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| CN110299985A (en) * | 2019-05-15 | 2019-10-01 | 西安理工大学 | A kind of fractional order broad sense memristor chaos circuit based on single fractional order inductance |
| CN113112010A (en) * | 2021-04-29 | 2021-07-13 | 齐鲁工业大学 | Nerve fiber equivalent circuit supporting soliton wave conduction |
| CN114528794A (en) * | 2022-02-14 | 2022-05-24 | 江西理工大学 | Fractional order chaotic circuit design method based on mixed memristor |
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| CN113112010A (en) * | 2021-04-29 | 2021-07-13 | 齐鲁工业大学 | Nerve fiber equivalent circuit supporting soliton wave conduction |
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