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4.2 Matlab
1.
>restart;
>with(plots);
>n:=0.2;
>x0:= 1.3;
>y0:=0.5;
>x[0]:= 1.35;
>y[0]:=.5;
>lambda:= 2.25;
>T:= 50.1;
>N:= 1000;
>tau:=0.5;
>alpha:=0.8;
>beta:= 1;
>A:= tau^(-alpha)/GAMMA(2-alpha);
1.896275757
>B:= tau^(-beta)/GAMMA(2-beta);
2.000000000
>x[1]:= x[0]*(1-lambda*n*(x[0]-1)*(y[0]-y0)/A);
1.35
>y[1]:= y[0]*(1+(1-n)*n*(x[0]-x0)*y[0]/B);
0.5010000000
>x[2]:= x[1]*(1-lambda*n*(x[1]-1)*(y[1]-y0)/A);
1.349887872
>y[2]:= y[1]*(1+(1-n)*n*(x[1]-x0)*y[1]/B);
0.5020040040
>for j from 2 to N-1 do
x[j+1]:=x[j]*(1-lambda*n*(x[j]-1)*(y[j]-y0)/A)-(sum(((1+k)^(1-alpha)-k^(1-alpha))*(x[j-k+1]-x[j-k]), k = 1.. j-1));
y[j+1]:=y[j]*(1+(1-n)*n*(x[j]-x0)*y[j]/B)-(sum(((1+k)^(1-beta)-k^(1-beta))*(y[j-k+1]-y[j-k]), k = 1.. j-1))
end do;
>R:= seq([x[j], y[j]], j = 0.. N-1);
>pointplot([R], style = line);
2.
>restart;
>with(plots);
>n:=0.2;
>x0:= 1.3;
>y0:=.5;
>x[0]:= 1.35;
>y[0]:=0.5;
>lambda:= 2.25;
>T:= 50;
>N:= 1250;
>tau:= 0.4e-1;
>alpha:=0.8;
>beta:=0.8;
>delta:=.5;
>omega:= 2;
>evalf(T/N);
>A:= tau^(-alpha)/GAMMA(2-alpha);
14.30307787
>B:= tau^(-beta)/GAMMA(2-beta);
14.30307787
>x[1]:= x[0]*(1-lambda*n*(x[0]-1)*(y[0]-y0)/A);
1.35
>y[1]:=y[0]*(1+(1-n)*n*(x[0]-x0)*y[0]/B)+evalf(delta*cos((0*omega)*tau));
1.000139830
>x[2]:= x[1]*(1-lambda*n*(x[1]-1)*(y[1]-y0)/A);
1.342565081
>y[2]:= y[1]*(1+(1-n)*n*(x[1]-x0)*y[1]/B)+evalf(delta*cos(omega*tau));
1.499100159
>for j from 2 to N-1 do
x[j+1]:=x[j]*(1-lambda*n*(x[j]-1)*(y[j]-y0)/A)-(sum(((1+k)^(1-alpha)-k^(1-alpha))*(x[j-k+1]-x[j-k]), k = 1.. j-1));
y[j+1]:=y[j]*(1+(1-n)*n*(x[j]-x0)*y[j]/B)-(sum(((1+k)^(1-beta)-k^(1-beta))*(y[j-k+1]-y[j-k]), k = 1.. j-1))+evalf(delta*cos(j*omega*tau))
end do;
>R:= seq([x[j], y[j]], j = 0.. N-1);
>RR:= seq([j*tau, x[j]], j = 0.. N-1);
>pointplot([RR], style = line);
>pointplot([R], style = line);
3.
>restart;
>with(plots);
>n:=0.2;
>x0:= 1.3;
>y0:=0.5;
>x[0]:= 1.35;
>y[0]:=0.5;
>lambda:= 2.25;
>T:= 500;
>N:= 5000;
>tau:= 0.4e-1;
>alpha:= 1;
>beta:= 1;
>delta:= 0.1e-1;
>omega:= 1;
>evalf(T/N);
>A:= tau^(-alpha)/GAMMA(2-alpha);
25.00000000
>B:= tau^(-beta)/GAMMA(2-beta);
25.00000000
>x[1]:= x[0]*(1-lambda*n*(x[0]-1)*(y[0]-y0)/A);
1.35
>y[1]:= y[0]*(1+(1-n)*n*(x[0]-x0)*y[0]/B)+evalf(delta*cos((0*omega)*tau));
0.5100800000
>x[2]:= x[1]*(1-lambda*n*(x[1]-1)*(y[1]-y0)/A);
1.349914270
>y[2]:= y[1]*(1+(1-n)*n*(x[1]-x0)*y[1]/B)+evalf(delta*cos(omega*tau));
0.5201552594
>for j from 2 to N-1 do
x[j+1]:=x[j]*(1-lambda*n*(x[j]-1)*(y[j]-y0)/A)-(sum(((1+k)^(1-alpha)-k^(1-alpha))*(x[j-k+1]-x[j-k]), k = 1.. j-1));
y[j+1]:= y[j]*(1+(1-n)*n*(x[j]-x0)*y[j]/B)-(sum(((1+k)^(1-beta)-k^(1-beta))*(y[j-k+1]-y[j-k]), k = 1.. j-1))+evalf(delta*cos(j*omega*tau))
end do;
>R:= seq([x[j], y[j]], j = 0.. N-1);
>RR:= seq([j*tau, x[j]], j = 0.. N-1);
>pointplot([RR], style = line);
>pointplot([R], style = line);
, , , , , .. , , , .
- .
.. , - , , .
. , , , , .
, :
- - ;
- , ;
- , ;
- ;
- ;
- ;
- ;
- .
, , .
1. , . : // . 1992. 10. 17-19.
2. .. // . 1995. .7. 6. . 65-74.
3. , .. . . . .: . 1988. . 112-135.
4. , .. . . .: . 2004. 82-91.
5. .. . . . / . . .. : , 2012. 179-188.
6. . . ( .. ) // . 1993. 5. . 82-91.
7. .., .. . .: , 1928. 287 .
8. , .., , .. . .: . 1989. . 145-149.
9. .. - // . - . 2014. 1(8). . 66-70.
10. .. . .: , 2003. 272 .
11. .. // . 2012. . 14. 1. . 124-127.
12. .. . -: . , 2015. 178 .
13. Boleantu M. Fractional dynamical systems and applications in economy // Differential Geometry - Dynamical Systems. Vol.10. 2008. pp. 62-70.
14. Krelle W. (Ed) The Future of the World Economy. Berlin. Springer-Verlad. 1990. b.101.
15. Yiding Y., Lei H., Guanchun L. Modeling and application of new nonlinear fractional financial model // Journal of Applied Mathematics. 2013
16. Tejado I., Duarte V., Nuno V. Fractional Calculus in Economic Growth Modeling. The Portuguese case. Conference: 2014 International Conference on Fractional Differentiation and its Applications (FDA'14).
17. Mendes R.V. A fractional calculus interpretation of the fractional volatility model // Nonlinear Dyn. 2008.
18. Mensch. G. Stalemate in Technology. Innovations Overcome the Depression Cambrg. Ballinger Pub Co. 1979. 241 p.
19. Mesarovic M., Pestel E. (Eds) Multilevel Computer Model of World Development System. Laxenburg: IIASA. 1974: b 60-65.
20. Zhenhua H., Xiaokang T. A new discrete economic model involving generalized fractal derivative // Advances in Difference Equations. 2015. V. 65. DOI 10.1186/s13662-015-0416-8.
21. .., .., .. // . - . 2012. 2(5). . 33-36.
22. .., .., .. // . - . 2012. 2(5). . 37-41.
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( ) | . 6: - , -, 03-06 2016 . / . . . . , . . ; . . -: . , 2016. . 38-40. | 6 | .. | |||||||
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