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////////////////////////////////////////////////////////////////////////////
// Model silnikov.cc SIMLIB
//
// Silnikov equation:
//
// dx1/dt = x2
// dx2/dt = x3
// dx3/dt = -a*x3 - x2 + b*x1*(1 - c*x1 - d*x1*x1)
//
// where a=0.4, b=0.65, c=0, and d=1 are parameters
// initial conditions of x1(0) = 0.1234, x2(0)=0.2, x3(0)=0.1
// output for Gnuplot
//
// SOURCE: Fishwick
//
// PerPet 1996, 2006
#include "simlib.h"
#include <iostream>
#include <cmath>
using namespace std;
const double StepPrn = 0.05; // step of output
class Silnikov {
public:
Parameter a,b,c,d;
Integrator x1, x2, x3;
Silnikov(double _a, double _b, double _c, double _d) :
a(_a), b(_b), c(_c), d(_d),
x1(x2, 0.1234),
x2(x3, 0.2),
x3(-a*x3 - x2 + b*x1*(1 - c*x1 - d*x1*x1), 0.1) {}
};
Silnikov e(0.4, 0.65, 0, 1);
// output sampling:
void Sample() {
cout << Time << ' ' << e.x1.Value() << ' ' << e.x2.Value() << '\n';
}
Sampler S(Sample, StepPrn);
// experiment description:
int main() {
cout << "# Silnikov equation output \n";
SetStep(1e-8,1e-3); // set step size range
Init(0,250); // experiment initialization
Run(); // simulation
}
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Next two plots can be created by Gnuplot script
(output data are stored in "silnikov.dat"):
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set nokey
set style data lines
set terminal png large; set output "silnikov.png"
set title "Silnikov equation, RKE method, maxstep = 1e-3"
plot [][-1.6:1.6] "silnikov.dat"
set terminal png large; set output "silnikov-phase.png"
set title "Silnikov equation, RKE method, maxstep = 1e-3"
plot [-1.6:1.6][-1.6:1.6] "silnikov.dat" using 2:3
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![[result1]](silnikov.png)
![[result2]](silnikov-phase.png)
Accumulated errors change the computed results for various integration methods
(clearly visible at time > 200; it depends on precision of arithmetic - the
result is for 32 bit code on i686 architecture):
![[result-methods]](silnikov-methods.png)
Last modification:
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