CN101291212A - Chaos signal with multiple scrolls generating method, and chaos signal generator - Google Patents

Abstract

The invention relates to a method of producing multi-scroll chaotic signals and a chaotic signal generator. The method is to add non-consecutive saturation functions in the x direction and the y direction of a linear switching system containing disturbance terms so as to produce n-scroll chaotic signals and n x m-scroll chaotic signals containing well-shaped attractors (n and m are natural numbers more than 1) and the number and the position of the attractors can be freely controlled by parameters. The chaotic signal generator is a multi-scroll chaotic signal generator which is made according to the method. The method can provide various forms, more complicated and highly-random chaotic signals so as to enable people to investigate the chaotic mechanism and characteristics more deeply.

Description

A kind of multi-scroll chaotic signals production method and chaos signal generator

Technical field

The present invention relates to a kind of chaotic signal producing method and generator, particularly about a kind of multi-scroll chaotic signals production method and chaos signal generator that contains well shape attractor.

Background technology

People originate in the sixties in 20th century to Research on Chaotic Phenomena, and Lorentz lorentz has found famous " buterfly effect " in research earth atmosphere process, opened the understanding of people to chaos phenomenon.Along with going deep into of research, it is found that chaotic signal to features such as initial value sensitiveness, randomness and continuous wide band power spectrum, these features make chaos have been widely used at aspects such as communication every field such as message transmission, coding, safety, thereby the generation of chaotic signal and control also more and more become the important directions of studying in the chaos phenomenon.Nineteen eighty-three, Chua has proposed famous cai's circuit first, and he produces the most effective of advanced dynamic behavior and one of simple chaotic oscillating circuit up to now in nonlinear circuit.By change, very abundant chaotic phenomenon such as can produce from period doubling bifurcation, single scrollwork, cycle 3 to two scrollworks, thereby people can be studied chaos mechanism and characteristic comparatively easily the cai's circuit parameter.Suykens and Vandewalle have introduced some non-smooth and discontinuous functions on the basis of cai's circuit, obtained multi-scroll chaotic signals not only on numerical simulation, and in side circuit.But up to now, the multi-scroll chaotic signals of this generation all is to contain the helical form attractor, and the attractor of other type seldom finds, for example our butterfly-like Lorentz lorentz's attractor of knowing.And the attractor with more complicated form is more extensive with respect to the helical form attractor in application facet corresponding to the stronger signal of randomness.

Chinese patent application CN1790979 discloses a kind of chaotic signal producing method, has provided a kind of method by linear switching systems generation chaos, has designed a kind of novel chaos generator.Be characterized in that Mathematical Modeling is simple, realize easily, and can produce chaos on the parameter yardstick very widely.But shortcoming is the chaotic signal of its generation only contains the single suction introduction, and randomness is strong inadequately.

Summary of the invention

The object of the invention provide one kind of multiple forms, more complicated, have height random and contain the multi-scroll chaotic signals production method and the chaos signal generator of well shape attractor.

For achieving the above object, the present invention takes following technical scheme: a kind of multi-scroll chaotic signals production method, and it may further comprise the steps:

1) adopt a linear switching systems that contains disturbance term, its function expression is:

$\left\{\begin{array}{c}\stackrel{\·}{x}=\mathrm{ay}\\ \stackrel{\·}{y}=-\mathrm{bx}+c_{h\left(z\right)}y\\ \stackrel{\·}{z}=d_{h\left(z\right)}+g_{h\left(z\right)}\left(x\right)\end{array}\right.$

G wherein _{H (z)}(x) be disturbance term, h (z) is a magnetic hysteresis switching function, is defined as:

$h\left(z\right)=\left\{\begin{array}{c}0,z\&le;z_1;\\ h\left(z^{-}\right),z_1<z<{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">z</figure-callout>}}_2;\\ 1,z\&GreaterEqual;z_2;\end{array}\right.$

2) x of the switched system that provides in step 1), add discrete saturation function item respectively, and then set up a compound switched system model on the y direction:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{ay}-\frac{f(y;{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_2,{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">q</figure-callout>}}_2,k_2,h_2)}{c}\\ \stackrel{\&CenterDot;}{y}=-\mathrm{bx}+c_{h\left(z\right)}y+f(x;{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="A20081010510500101.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A20081010510500101.png,A20081010510500121.png"\; state="\{\{state\}\}">q</figure-callout>}}_1,k_1,h_1)-\frac{f(y;{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_2,{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">q</figure-callout>}}_2,k_2,h_2)}{a}\\ \stackrel{\&CenterDot;}{z}=d_{h\left(z\right)}+g_{h\left(z\right)}\left(x\right)\end{array}\right.;$

3) the said system model is carried out numerical solution, obtain chaotic signal at x, two groups of numerical value on the y direction, and form many scrollworks attractor in the plane;

4) according to said system modelling circuit to produce multi-scroll chaotic signals.

Described saturation function expression formula is:

$f(x;p,q,k,h)=\left\{\begin{array}{cc}(2q+1)k,& x>\mathrm{qh}+1\\ k(x-\mathrm{ih})+2\mathrm{ik},& |x-\mathrm{ih}|\&le;1,-p\&le;i\&le;q;\\ (2i+1)k,& \mathrm{ih}+1<x<(i+1)h-1,-p\&le;i\&le;q-1;\\ -(2p+1)k,& x<-\mathrm{ph}-1\end{array}\right.$

If p=q=0, described saturation function expression formula is:

$f(x;k)=\left\{\begin{array}{cc}k,& x>1\\ \mathrm{kx},& \left|x\right|\&le;1\\ -k,& x<-1\end{array}\right.$

If get f (y; p ₂, q ₂, k ₂, h ₂)=0 then produces p in the x direction ₁+ q ₁+ 2 scrollwork attractors; If get f (y; p ₂, q ₂, k ₂, h ₂) ≠ 0, then at x, the y plane produces (p ₁+ q ₁+ 2) * (p ₂+ q ₂+ 2) lattice scroll chaotic signals, each described scrollwork all contains well shape attractor, and by regulating the parameter of described saturation function, can determine the number and the position of attractor.

A kind of multi-scroll chaotic signals generator that adopts said method to make.

The present invention is owing to take above technical scheme, it has the following advantages: 1, method of the present invention is to add discrete saturation function on the x of the linear switching systems that contains disturbance term and y direction, thereby can produce the n scroll chaotic signals that contains well shape attractor and the chaotic signal (wherein n and m are the natural numbers greater than 1) of n * m lattice scrollwork, and the number of attractor and position can freely be controlled by parameter, therefore can provide variform, more complicated, and the chaotic signal with height random can more in depth be studied people to chaos mechanism and characteristic.2, because therefore system model of the present invention can both can be used as the encryption equipment and the decipher of information easily by numerical simulation or electronic circuit realization, can be used as a kind of multi-functional chaos signal generator again.

Description of drawings

Fig. 1 a is the schematic diagram of switching signal of the present invention

Fig. 1 b is that the present invention represents to work as k=10, h=10, the saturation signal f (x during p=q=1; K, h, p, q)

Fig. 2 a is the 2 scroll chaotic signals x-y direction projection figure that the present invention produces

Fig. 2 b is the 2 scroll chaotic signals x-y direction projection enlarged drawings that the present invention produces

Fig. 3 a is the 4 scroll chaotic signals x-y direction projection figure that the present invention produces

Fig. 3 b is the 4 scroll chaotic signals x-y direction projection enlarged drawings that the present invention produces

Fig. 4 a is 2 * 2 scroll chaotic signals x-y direction projection figure that the present invention produces

Fig. 4 b is 4 * 4 scroll chaotic signals x-y direction projection enlarged drawings that the present invention produces

Fig. 5 is the attractor distribution map of system model behind the elapsed time t of the present invention

Fig. 6 is the hopping time distribution map of the present invention on the invariant space of different attractors

Embodiment

Below in conjunction with drawings and Examples of the present invention, describe the present invention.

Method of the present invention is to add discrete saturation function on the x of a linear switching systems that contains disturbance term and y direction, thereby produce and to contain the n scroll chaotic signals of well shape attractor and the chaotic signal (wherein n and m are the natural numbers greater than 1) of n * m lattice scrollwork, and the number of attractor and position can freely be controlled by parameter.The method that the chaotic signal of n scroll chaotic signals and n among the present invention * m lattice scrollwork produces may further comprise the steps:

1) adopt a linear switching systems that contains disturbance term, the function expression of this linear switching systems is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{ay}\\ \stackrel{\&CenterDot;}{y}=-\mathrm{bx}+c_{h\left(z\right)}y\\ \stackrel{\&CenterDot;}{z}=d_{h\left(z\right)}+g_{h\left(z\right)}\left(x\right)\end{array}\right.---\left(1\right)$

G wherein _{H (z)}(x) be disturbance term, h (z) is a magnetic hysteresis switching function, is defined as:

$h\left(z\right)=\left\{\begin{array}{c}0,z\&le;z_1;\\ h\left(z^{-}\right),z_1<z<{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">z</figure-callout>}}_2;\\ 1,z\&GreaterEqual;z_2;\end{array}\right.---\left(2\right)$

z ₁, z ₂Be positive constant, under this definition, system variable a, b, c ₀, c ₁, d ₀, d ₁, g ₀(x), g ₁(x) be taken as:

a＞0，b＞0，c ₀＝-c ₁＝c＞0，d ₀＝-d ₁＝d＞0，g ₀(x)＝0，g ₁(x)＝εsin?x，|ε|＜dz ₁。

Add discrete saturation function item on the x of the switched system that 2) in step 1), provides and the y direction, and then set up a compound switched system model (hereinafter to be referred as system model):

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{ay}-\frac{f(y;{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_2,{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">q</figure-callout>}}_2,k_2,h_2)}{c}\\ \stackrel{\&CenterDot;}{y}=-\mathrm{bx}+c_{h\left(z\right)}y+f(x;{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="A20081010510500101.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A20081010510500101.png,A20081010510500121.png"\; state="\{\{state\}\}">q</figure-callout>}}_1,k_1,h_1)-\frac{f(y;{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_2,{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">q</figure-callout>}}_2,k_2,h_2)}{a}\\ \stackrel{\&CenterDot;}{z}=d_{h\left(z\right)}+g_{h\left(z\right)}\left(x\right)\end{array}\right.---\left(3\right)$

F (x; P, q, k is discontinuous saturation function h), is defined as:

$f(x;p,q,k,h)=\left\{\begin{array}{cc}(2q+1)k,& x>\mathrm{qh}+1\\ k(x-\mathrm{ih})+2\mathrm{ik},& |x-\mathrm{ih}|\&le;1,-p\&le;i\&le;q;\\ (2i+1)k,& \mathrm{ih}+1<x<(i+1)h-1,-p\&le;i\&le;q-1;\\ -(2p+1)k,& x<-\mathrm{ph}-1\end{array}\right.---\left(4\right)$

If p=q=0, then f (x; K) be expressed as: $f(x;k)=\left\{\begin{array}{cc}k,& x>1\\ \mathrm{kx},& \left|x\right|\&le;1\\ -k,& x<-1\end{array}\right..$

3) to step 2) in obtain system model and carry out numerical solution, the method of numerical solution can use conventional matlab to find the solution, and also can be to program voluntarily to find the solution, and has obtained chaotic signal at x, two groups of numerical value on the y direction, and form many scrollworks attractor in the plane.

4) according to said system modelling circuit to produce multi-scroll chaotic signals.

Below in conjunction with system model, the generating process of the multi-scroll chaotic signals that comprises well shape attractor is analyzed:

For system model, at first analyze the situation that attractor only produces in the x direction, this moment, we got f (y; p ₂, q ₂, k ₂, h ₂)=0, this moment, there were two class balance points in system as can be seen:

$U_x=\{\frac{(-2({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="A20081010510500101.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_1+1)+1)k_1}{b},\frac{(-2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="A20081010510500101.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_1+1)k_1}{b},...,\frac{(2{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A20081010510500101.png,A20081010510500121.png"\; state="\{\{state\}\}">q</figure-callout>}}_1+1)k_1}{b}\}---\left(5\right)$

$V_x=\{\frac{-2p_1{k}_1}{b},\frac{-2(p_1-1)k_1}{b},...,\frac{2q_1{k}_1}{b}\}---\left(6\right)$

For x, the y direction, characteristic equation is λ ²+ c λ+ab=0, here we get c ²-4ab＜0 can guarantee that the equilbrium position is unsettled, thereby produces chaos.For first kind balance point U _x, f (x; p ₁, q ₁, k ₁, h ₁) always remain unchanged within the specific limits, can guarantee that therefore the track of system model forms stable attractor in this type of balance point place vibration.And for the second class balance point V _x, f (x; p ₁, q ₁, k ₁, h ₁) state that becomes when being in, the balance point instability that form this moment, thereby just play the effect that connects first kind balance point.So for system model at f (y; p ₂, q ₂, k ₂, h ₂Under the situation of)=0, can produce by p ₁+ q ₁+ 1 p that tie point connects ₁+ q ₁+ 2 scrollwork attractors, and the position of attractor can arbitrarily be adjusted.

Similarly, for f (y; p ₂, q ₂, k ₂, h ₂The situation of) ≠ 0 also can obtain two class balance points in the y direction:

$U_y=\{\frac{(-2({\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_2+1)+1){\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{ac}},\frac{(-2{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">p</figure-callout>}}_2+1){\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{ac}},...,\frac{(2{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">q</figure-callout>}}_2+1){\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{ac}}\}---\left(7\right)$

$V_y=\{\frac{-2p_2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{ac}},\frac{-2(p_2-1){\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{ac}},...,\frac{2q_2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{\mathrm{ac}}\}---\left(8\right)$

Can produce in the y direction equally by p ₂+ q ₂+ 1 p that tie point connects ₂+ q ₂+ 2 scrollwork attractors, comprehensive x direction, at x, the y plane just can produce (p ₁+ q ₁+ 2) * (p ₂+ q ₂+ 2) lattice scrollwork attractor.

The following describes the motion conditions of system model track.

The variation track figure of magnetic hysteresis signal h (z) has been described as shown in Figure 1a; Shown in Fig. 1 b, described and worked as k=10, h=10, the variation track figure of discrete saturation function during p=q=1.

Given initial condition X ₀=(x ₀, y ₀, z ₀) ^T, z ₀∈ [z ₁, z ₂] and the initial value h (z (0))=0 of switching signal, by $\stackrel{\&CenterDot;}{z}=\mathrm{cz},$ The track of system model begins to rise along z axle positive direction; When it touches plane z=z ₂The time, the switching signal h of system model (z) changes to 1 from 0; This moment is because the parameter that we select $\left|\mathrm{\&epsiv;}\right|<{\mathrm{<figure-callout\; id="1"\; label="dz"\; filenames="A20081010510500101.png,A20081010510500121.png"\; state="\{\{state\}\}">dz</figure-callout>}}_1\&RightArrow;\stackrel{\&CenterDot;}{z}=\mathrm{\&epsiv;}\sin x-{\mathrm{<figure-callout\; id="2"\; label="cz"\; filenames="A20081010510500104.png,A20081010510500121.png"\; state="\{\{state\}\}">cz</figure-callout>}}_2\&le;\left|\mathrm{\&epsiv;}\right|-{\mathrm{cz}}_2<\left|\mathrm{\&epsiv;}\right|-{\mathrm{cz}}_1<0,$ Thereby track begins to descend along z axle negative direction, up to meeting plane z=z ₁, switching signal h (z) changes to 0 from 1, thus track rises once more; Therefore system model always switches in the middle of these two states repeatedly.To x, the motion conditions on y plane is supposed at initial time $\stackrel{\&CenterDot;}{x}>0,$ $\stackrel{\&CenterDot;}{y}>0,$ X, the size of y begins all to move toward positive direction, and the balance point of this moment is assumed to (x ₁, y ₁), As time goes on, switching appears in system model, and y moves toward negative direction, moves toward negative direction thereby drive x, because the uncertainty of switching may be crossed balance point (x ₁, y ₁), this moment, switching appearred in system model once more, x then, y moves toward positive direction again, and in this handoff procedure if x, y enters another balance point (x ₂, y ₂) scope, the track of system model is just at (x ₂, y ₂) motion on every side, the chaos phenomenon that just occurs many scrollworks repeatedly like this.

Shown in Fig. 2 a, Fig. 2 b, be respectively 2 scroll chaotic signals x-y direction projection figure and enlarging projection figure of generation, parameter value is respectively a=2 here, b=1, c=0.5, d=0.6, ε=1, z ₁=2, z ₂=15, k=10, p=q=0.

Shown in Fig. 3 a, Fig. 3 b, be respectively 4 scroll chaotic signals x-y direction projection figure and enlarging projection figure of generation, parameter value is respectively a=2 here, b=1, c=0.5, d=0.6, ε=1, z ₁=2, z ₂=15, h=k=10, p=q=1.

Shown in Fig. 4 a, be 2 * 2 lattice scroll chaotic signals x-y direction projection figure that produce, parameter value is respectively here:

a＝2，b＝4，c＝0.5，d＝0.6，ε＝1，z ₁＝2，z ₂＝15，k ₁＝40，P ₁＝q ₁＝0，k ₂＝5，p ₂＝q ₂＝0

Shown in Fig. 4 b, be 4 * 4 lattice scroll chaotic signals x-y direction projection figure that produce, parameter value is respectively here:

a＝2，b＝4，c＝0.5，d＝0.6，ε＝1，z ₁＝2，z ₂＝15，h ₁＝20，k ₁＝40，p ₁＝q ₁＝1，h ₂＝5，k ₂＝5，p ₂＝q ₂＝1。

From above-mentioned various scroll chaotic signals x-y direction projection figure and enlarged drawing, we can clearly see the scrollwork attractor, and by enlarged drawing as can be seen these attractors are well shape attractors.

As shown in Figure 5, when having provided signal among the figure and having contained 20 scrollworks under the value of 1000 different initial conditions, system model is the situation of occupying of end each attractor during time t (being defined as at the end constantly, the track of t system model is positioned near the attractor i), the sequence number i of x direction indication attractor (with-10 to 10 expressions), the y direction indication at the end constantly the track of t system model be positioned at the different initial value number N of attractor i, the mark of system's rail model is uniformly distributed in each attractor when t increases as can be seen.

As shown in Figure 6, provided near the jump distribution map (being defined as the time interval between two paroxysms of x variable) of when signal contains 3 scrollworks system model x variable each attractor n (n=-1,0,1) among the figure, the x direction indication is to the time interval t γ that takes the logarithm _t, the y direction indication is to the time of occurrence probability of the t ρ that takes the logarithm at interval _γ, all meet the rule ρ that a logarithm distributes as can be seen _γ=γ ^-1.5Fig. 5, Fig. 6 show that the movement locus of the system model among the present invention has sizable randomness, meets the feature of chaotic signal.

Although disclose preferred embodiment of the present invention and accompanying drawing for the purpose of illustration, its purpose is to help to understand content of the present invention and implement according to this, but person skilled in the art, without departing from the spirit and scope of the invention and the appended claims, can do various replacements, variation and retouching.Therefore, the present invention should not be limited to most preferred embodiment and the disclosed content of accompanying drawing, and protection scope of the present invention is as the criterion with the scope that appending claims was defined.

Claims (5)

1, a kind of multi-scroll chaotic signals production method, it may further comprise the steps:

1) adopt a linear switching systems that contains disturbance term, its function expression is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{ay}\\ \stackrel{\&CenterDot;}{y}=-\mathrm{bx}+c_{h\left(z\right)}y\\ \stackrel{\&CenterDot;}{z}=d_{h\left(z\right)}+g_{h\left(z\right)}\left(x\right)\end{array}\right.$

G wherein _{H (z)}(x) be disturbance term, h (z) is a magnetic hysteresis switching function, is defined as:

$h\left(z\right)=\left\{\begin{array}{c}0,z\&le;z_1;\\ h\left(z^{-}\right),z_1<z<z_2\\ 1,z\&GreaterEqual;z_2;\end{array}\right.$

2) on the x of the switched system that step 1) provides and y direction, add discrete saturation function item respectively, and then set up a compound switched system model:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\mathrm{ay}-\frac{f(y;p_2,q_2,k_2,h_2)}{c}\\ \stackrel{\&CenterDot;}{y}=-\mathrm{bx}+c_{h\left(z\right)}y+f(x;p_1,q_1,k_1,h_1)-\frac{f(y;p_2,q_2,k_2,h_2)}{a}\\ \stackrel{\&CenterDot;}{z}=d_{h\left(z\right)}+g_{h\left(z\right)}\left(x\right)\end{array}\right.$

3) the said system model is carried out numerical solution, obtain chaotic signal at x, two groups of numerical value on the y direction, and form many scrollworks attractor in the plane;

4) according to said system modelling circuit to produce multi-scroll chaotic signals.

2, a kind of multi-scroll chaotic signals production method as claimed in claim 1, it is characterized in that: described saturation function expression formula is:

$f(x;p,q,k,h)=\left\{\begin{array}{cc}(2q+1)k,& x>\mathrm{qh}+1\\ k(x-\mathrm{ih})+2\mathrm{ik},& |x-\mathrm{ih}|\&le;1,-p\&le;i\&le;q;\\ (2i+1)k,& \mathrm{ih}+1<x<(i+1)h-1,-p\&le;i\&le;q-1;\\ -(2p+1)k,& x<-\mathrm{ph}-1\end{array}\right.$

3, a kind of multi-scroll chaotic signals production method as claimed in claim 2 is characterized in that: if p=q=0, described saturation function expression formula is:

$f(x;k)=\left\{\begin{array}{cc}k,& x>1\\ \mathrm{kx},& \left|x\right|\&le;1\\ -k,& x<-1\end{array}\right.$

4, a kind of multi-scroll chaotic signals production method as claimed in claim 1 or 2 is characterized in that: if get f (y; p ₂, q ₂, k ₂, h ₂)=0 then produces p ₁+ q ₁+ 2 scrollwork attractors; If get f (y; p ₂, q ₂, k ₂, h ₂) ≠ 0 then produces (p ₁+ q ₁+ 2) * (p ₂+ q ₂+ 2) lattice scroll chaotic signals, each described scrollwork all contains well shape attractor, and by regulating the parameter of described saturation function, can determine the number and the position of attractor.

5, a kind of multi-scroll chaotic signals generator of making as method as described in the claim 1～4 that adopts.

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