CN108768609A - A kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics - Google Patents
A kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention discloses a kind of analysis methods of similar frequency dependence time delay electric light phase chaotic dynamics, carry out as follows：The first step：Establish the dynamic mathematical models in chaotic communication system；Second step：Determine the relationship of delay and frequency；Third walks：It divides time interval and determines equation initial value；4th step：It is converted by Fourier's T/F, finds out certain a period of time each moment time delayed signal after delay；5th step：Convert Delay Differential Equations to ODE；6th step：Numerical solution is carried out using the ODE of the 5th step of Runge-Kutta methods pair.The present invention can accurately solve the Integro-differential equations with frequency dependence time delay, and accurately analysis has frequency dependence time delay feedback chaotic dynamics and chaotic communication.
Description
Technical field
The invention belongs to optical information technology fields, and in particular to a kind of similar frequency dependence time delay electric light phase chaos power
Analysis method.
Background technology
In current chaotic optical communication system, is usually intercoupled using semiconductor laser and increase its degree of freedom to generate
Chaotic signal.Its maximum feature is the carrier wave using chaotic signal as signal, is synchronized and robustness since chaos has
Feature realizes the decoding of transmission information.When transmitting signal, the chaotic carrier of transmitter output acts as the load of transmission signal
Body.It is difficult to separate signal from chaotic carrier since the amplitude of signal is much smaller than the fluctuation of chaotic carrier.Specifically
Ground is said, for decoded signal, transmission information needs receiver similar with transmitter height to be coupled.Only produced in receiver
It could be exported by monitoring receiver and input in the case that raw chaotic carrier is synchronous with the chaotic carrier that transmitter generates
Synchronous error restores signal.Therefore, Chaotic Synchronous is the key that realize entire chaos Transmission system.Receiver and transmitter object
Reason parameter is identical, and the two achieves that synchronization.To prevent from eavesdropping, the parameter of transmitting terminal must stash, and cannot obtain transmitter
Parameter can not just reconstruct the chaotic dynamics of transmitting terminal, ensure that the safety of communication.This namely frequency dependence delay time
The hiding chaos safety communicating method of signature.
The present invention is directed to similar frequency dependence time delay electric light phase differential-integral equation, provides a kind of similar frequency phase
Close the analysis method of time delay electric light phase chaotic dynamics.
Invention content
For the general differential identity expression with delay and feedback, the present invention is to above-mentioned electro-optical feedback chaotic communication
There is the encrypted frequency dependence delay time signature of digital secret key to hide to be studied in system, to this kind of mixed with electro-optical feedback
Ignorant communication system establishes system model, provide it is a kind of based on frequency dependence be delayed and feed back differential identity expression,
Analyze the kinetic characteristics of frequency dependence delay electric light phase chaos.This is also further to synchronize to lay the first stone for system realization.
The present invention takes following technical scheme：
A kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics, carries out as follows：
The first step：Establish the dynamic mathematical models in chaotic communication system；
Second step：Determine the relationship of delay and frequency；
Third walks：It divides time interval and determines the Integro-differential equations initial value of description electric light phase chaos；
4th step：The signal after delay is found out using Fourier's time-frequency conversion；
5th step：Convert Delay Differential Equations to ODE；
6th step：Numerical solution is carried out to ODE using Runge-Kutta methods.
Further, the specific method is as follows for the first step：
Transmitting terminal part in chaotic communication system is modeled, system carries out phase using Mach-Zehnder interferometers
Modulation, transmitting terminal equation are：
Wherein, τ and θ is higher cutoff frequency and the low cutoff frequency corresponding response time of backfeed loop respectively, and G is that electricity is put
Big device gain, φ is initial phase, and x, t indicate phase and time respectively.
Further, the specific method is as follows for the second step：
Delay with frequency dependence is generated by ring resonator, and transmission equation is：
And
A3=A4ejβL (4)
Wherein r and k is the coefficient of coup of ring resonator,It is transmission, n is refractive index, and ω is optical frequency
Rate, c are the lighies velocity, and L is that chamber is long, and j is complex unit, A1With A2Relationship be：
Transfer function is expressed as
H (ω) is expressed as to the form of amplitude and frequency, i.e.,
H (ω)=| H (ω) | eiφ (7)
Wherein φHIt is the phase of H (ω), the delay with frequency dependence is then expressed as
Further, the specific method of the third step is：
N sections will be divided into total time T, every time is longRespectively to each period according to formula (1)-(2)
The value for the last moment for being solved, and a upper period being solved brings lower a period of time into as the initial value of subsequent time
Between section solved, operation is repeated in this way, until will solve equation in time T；For the initial of first Δ T
Value enables the integral in the differential equation (1) and (2) be equal to 0, then finds out the stable solution of equation, then regard this solution as first
The initial value of Δ T.
Further, the specific method of the 4th step is：
Mentioned above, the present invention, which is directed to, solves the Delay Differential Equations with frequency dependence, it is contemplated that this delay
With frequency dependence, that is just handled on frequency domain.
Following equation 9 and 10 respectively represents [x1(t)+x2(t)]、[x2(t)] after being delayed by, the contravariant of Fourier transformation
It changes.
x22(t)=x2(t-δT-τf)=ifft { fft [x2(t)]·e-jωδT} (10)
Wherein, fft represents Fourier transformation, and ifft represents Fourier inversion, φHIt is ring resonator transfer function H
The phase of (ω).
Further, the specific method of the 5th step is：
The present invention considers in transmission process, due to x1With x2Signal after delay solves in the 4th step, that for
Equation originally has also reformed into ODE, as follows
Further, the Runge-Kutta methods are known equation derivative and Initial Information, when using Computer Simulation,
The process for solving the differential equation is saved, the process is specific as follows：
For containing initial problem generality equation：
y′i=fi(t,y1y2·yi··yn),yi(t0)=yi(0), i=1,2, n, n indicate the number of equation.
It is obtained by fourth-order Runge-Kutta method
H indicates time interval.
Wherein
k1=fj(tj,yj)
In this way, next value (yi,j+1) by present value (yi,j) add multiplying for the slope that time interval (h) is estimated with one
Product determines.The slope is the weighted average of following slope：
●k1It is slope when starting the period；
●k2It is the slope at period midpoint, slope k is used by Euler method1To determine y in point tnThe value of+h/2；
●k3It is also the slope at midpoint, but specifically uses slope k2Determine y values；
●k4It is the slope of time segment endpoint, y values k3It determines.
Compared with prior art, the invention has the advantages that：
1, the present invention proposes processing with the solution with the time delayed signal of frequency dependence.
2, the present invention can also analyze chaotic signal Temporal Evolution characteristic.
3, the present invention plays the role of the chaotic communication system of the hiding digital signature of analysis bigger.
Description of the drawings
Fig. 1 is the analysis process figure of the present invention.
Fig. 2 is the structural schematic diagram of the corresponding communication system of the present invention.
The upper figures of Fig. 3 are transmitting terminal luminous power time series chart, and middle figure is receiving terminal luminous power time series chart, and figure below is hair
The difference power of sending end and receiving terminal.Show that receiving terminal is in transmitting terminal in strictly synchronous.
The upper figures of Fig. 4 are transmitting terminal phase time sequence chart, and middle figure is receiving terminal light phase time series chart, and figure below is to send
The phase difference at end and receiving terminal.Also indicate that receiving terminal is in transmitting terminal in strictly synchronous.
Fig. 5 is transmitting terminal luminous power auto-correlation coefficient figure.
The upper figures of Fig. 6 are the information of transmission, and figure below is the signal after demodulation.
Specific implementation mode
It elaborates below in conjunction with the accompanying drawings to the embodiment of the present invention.
The present embodiment carries out the analysis of similar frequency dependence time delay electric light phase chaotic dynamics according to the analysis process of Fig. 1
Method.Analysis method is as follows：
The first step：Establish the dynamic mathematical models in chaotic communication system.
The present invention models transmitting terminal part in chaotic communication system, system using Mach-Zehnder interferometers into
Row phase-modulation, transmitting terminal equation can be write as
Wherein, τ and θ is higher cutoff frequency and the low cutoff frequency corresponding response time of backfeed loop respectively, and G is that electricity is put
Big device gain, φ is initial phase.
Second step：Determine the relationship of delay and frequency.
In this communication system, the delay with frequency dependence is generated by ring resonator, and transmission equation is
And
A3=A4ejβL (4)
Wherein r and k is the coefficient of coup of ring resonator,It is transmission, n is refractive index, and ω is light frequency,
C is the light velocity, and L is that chamber is long, can obtain A1With A2Relationship.
Wherein transfer function can be expressed as
If H (ω) to be expressed as to the form of amplitude and frequency, i.e.,
H (ω)=| H (ω) | eiφ (7)
Wherein φHIt is the phase of H (ω), the delay of that and frequency dependence can be expressed as
Third walks：It divides time interval and determines equation initial value.
The present invention will be divided into N sections total time T, and every time is longThis method respectively carries out each period
It solved, and the value for the last moment that a upper period is solved brings subsequent time period into as the initial value of subsequent time
It is solved, operation is repeated in this way, until will solve equation in time T.It, can for the initial value of first Δ T
To enable the integral in the differential equation (1) and (2) be equal to 0, the stable solution of equation is then found out, then regard this solution as first Δ
The initial value of T.
4th step：The signal after delay is found out using Fourier's time-frequency conversion.
Mentioned above, the present invention, which is directed to, solves the Delay Differential Equations with frequency dependence, it is contemplated that this delay
With frequency dependence, that is just handled on frequency domain.
x22(t)=x2(t-δT-τf)=ifft { fft [x2(t)]·e-jωδT}
(10)
Wherein, fft represents Fourier transformation, and ifft represents Fourier inversion, φHIt is ring resonator above-mentioned
The phase of transfer function H (ω).
5th step：Convert Delay Differential Equations to ODE.
The present invention considers in transmission process, due to x1With x2Signal after delay solves in the 4th step, that for
Equation originally has also reformed into ODE, as follows
6th step：Numerical solution is carried out to ODE (11) and (12) using Runge-Kutta methods.
In the present embodiment, as shown in Fig. 2, after the continuous light of transmitting terminal laser generation 10mW, information passes through phase tune
Device processed carries out phase-modulation to continuous light, by having loss factor 0.082, the Mach-Zehnder that bias voltage is 4.1V dry
Interferometer, using 1:1 optical branching filter, arrives receiving terminal all the way, another way by the frequency dependence that is delayed, with maximum delay 76ps's
Optical circulator is cascaded, by 2ns time delay optical fibers, by the corresponding time 13.5ps of higher cutoff frequency and low cutoff frequency corresponding time
The photodetector of 5.5 μ s light converts optical signals into electric signal, and the electric amplifier for being 8 by gain amplifies, and feeds back to Mach-once
Dare interferometer refractive index is modulated, and realizes the phase-modulation of optical signal.It can be obtained using aforementioned calculation method defeated
The luminous power chaos time sequence gone out, the CHAOTIC PHASE sequence of optical signal.By the auto-correlation computation of signal, autocorrelation spectrum is found
In without apparent peak, referring to Fig. 5, without specific two peaks in figure, illustrate that delay time is hidden.Furtherly
The accuracy calculated in bright foregoing invention content.
In receiving terminal, the signal received is divided into two-way by channel-splitting filter, all the way by photoelectric detector, the electricity that gain is 12
Amplifier.Another way drives the electro-optic phase oscillation rings consistent with transmitting terminal structure and parameter, calculation shows that the luminous power generated
Chaos time sequence, phase chaos time sequence and transmitting terminal are fully synchronized, and calculating also shows：It is detected by photoelectric detector
Receiving terminal synchronizes optical signal, and the signal that the electric amplifier amplification detection for being 10 using gain comes out detected with the first via
Signal carries out calculus of differences, can accurately demodulate the information of transmission.Illustrate that this computational methods has powerful reliability.
The present invention can accurately solve the Integro-differential equations with frequency dependence time delay, and accurately analysis has
Frequency dependence time delay feedback chaotic dynamics and chaotic communication.
In this example implementation process, numerical computations are carried out by the above method, are obtained：When not adding transmission information, before Fig. 3
The luminous power time series chart of transmitting terminal and receiving terminal when two figures, rearmost figure is two difference powers, shows strictly to be in
In synchronizing；And the upper figures of Fig. 4 are transmitting terminal phase time sequence chart, middle figure is receiving terminal light phase time series chart, and figure below is hair
The phase difference of sending end and receiving terminal.Also indicate that receiving terminal is in transmitting terminal phase in strictly synchronous.The upper figures of Fig. 6 are transmitting terminal
The information added, figure below are to demodulate the information come.The above method calculation shows that, due to the robustness of system synchronization, not plus information
It is both ends stringent synchronization, in addition when information, in losing synchronous regime, therefore the information of transmitting terminal transmission can be restored.
The preferred embodiment of the present invention and principle are described in detail above, to those skilled in the art
Speech, the thought provided according to the present invention will change in specific implementation mode, and these changes also should be regarded as the present invention
Protection domain.
Claims (8)
1. a kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics, which is characterized in that this method is by such as
Lower step carries out：
The first step：Establish the dynamic mathematical models in chaotic communication system；
Second step：Determine the relationship of delay and frequency；
Third walks：It divides time interval and determines the Integro-differential equations initial value of description electric light phase chaos；
4th step：The signal after delay is found out using Fourier's time-frequency conversion；
5th step：Convert Delay Differential Equations to ODE；
6th step：Numerical solution is carried out to ODE using Runge-Kutta methods.
2. a kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics according to claim 1,
It is characterized in that, the specific method is as follows for the first step：
Transmitting terminal part in chaotic communication system is modeled, system carries out phase tune using Mach-Zehnder interferometers
System, transmitting terminal equation are：
Wherein, τ and θ is the higher cutoff frequency of backfeed loop respectively and low cutoff frequency corresponding response time, G are electric amplifiers
Gain, φ are initial phases, and x, t indicate phase and time respectively.
3. a kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics according to claim 1,
It is characterized in that, the specific method is as follows for the second step：
Delay with frequency dependence is generated by ring resonator, and transmission equation is：
And
A3=A4ejβL (4)
Wherein r and k is the coefficient of coup of ring resonator,It is transmission, n is refractive index, and ω is light frequency, and c is
The light velocity, L are that chamber is long, and j is imaginary unit, A1With A2Relationship be：
Transfer function is expressed as
H (ω) is expressed as to the form of amplitude and frequency, i.e.,
H (ω)=| H (ω) | eiφ (7)
Wherein φHIt is the phase of H (ω), the delay with frequency dependence is then expressed as
4. a kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics according to claim 1,
It is characterized in that, the specific method of the third step is：
N sections will be divided into total time T, every time is longEach period is carried out according to formula (1)-(2) respectively
It solved, and the value for the last moment that a upper period is solved brings subsequent time period into as the initial value of subsequent time
It is solved, operation is repeated in this way, until will solve equation in time T；For the initial value of first Δ T, enable
Integral in the differential equation (1) and (2) is equal to 0, then finds out the stable solution of equation, then by this solution as first Δ T's
Initial value.
5. a kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics according to claim 1,
It is characterized in that, the specific method of the 4th step is：
[x1(t)+x2(t)]、[x2(t)] after being delayed by, the inverse transformation of Fourier transformation is expressed as：
x22(t)=x2(t-δT-τf)=ifft { fft [x2(t)]·e-jωδT} (10)
Wherein, fft represents Fourier transformation, and ifft represents Fourier inversion, φHIt is ring resonator transfer function H (ω)
Phase.
6. a kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics according to claim 1,
It is characterized in that, the specific method of the 5th step is：
x1With x2Signal after delay solves in the 4th step, becomes ODE for original equation, as follows
7. a kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics according to claim 1,
It is characterized in that, the Runge-Kutta methods are known equation derivative and Initial Information, when using Computer Simulation, save solution
The process of the differential equation.
8. a kind of analysis method of similar frequency dependence time delay electric light phase chaotic dynamics according to claim 7,
It is characterized in that, the Runge-Kutta methods process is specific as follows：
For containing initial problem generality equation：
yi'=fi(t,y1y2·yi··yn),yi(t0)=yi(0), i=1,2, n, n indicate the number of equation；
It is obtained by fourth-order Runge-Kutta method
H indicates time interval；
Wherein
k1=fj(tj,yj)
Next value (yi,j+1) by present value (yi,j) determined plus time interval (h) and the product of the slope of an estimation, institute
State the weighted average that slope is following slope：k1It is slope when starting the period；k2It is the slope at period midpoint, passes through Europe
Daraf(reciprocal of farad) uses slope k1To determine y in point tnThe value of+h/2；k3It is also the slope at midpoint, slope k2Determine y values；k4It is end period
The slope of point, y values k3It determines.
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| CN112202462A (en) * | 2020-10-15 | 2021-01-08 | Oppo广东移动通信有限公司 | Time delay compensation method and device, electronic equipment and storage medium |
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