RSolve不解决离散Rossler系统

Question

我正在处理混沌吸引子,并测试一些连续的 - >离散的等价物.我用这种方式连续模拟了Rossler系统

a = 0.432; b = 2; c = 4;
Rossler = {
    x'[t] == -y[t] - z[t], 
    y'[t] == x[t] + a*y[t],
    z'[t] == b + x[t]*z[t]-c*z[t]};
sol = NDSolve[
  {Rossler, x[0] == y[0] == z[0] == 0.5}, 
  {x, y, z}, {t,500}, MaxStepSize -> 0.001, MaxSteps -> Infinity]

现在,当尝试使用RSolve评估离散等效系统时,Mma不做任何事情,甚至不是错误,它只是无法解决它.

RosslerDiscreto = {
       x[n + 1] == x[n] - const1*(y[n] + z[n]),
       y[n + 1] == 1 - a*const2)*y[n] + const2*x[n], 
       z[n + 1] == (z[n]*(1 - const3) + b*const3)/(1 - const3*x[n])}

我想知道RSolve是否有数值函数,类似于NDSolve用于DSolve.我知道我可以用一些For []循环进行计算,只想知道它是否存在这样的函数.

Answer 1

RecurrenceTable 是RSolve的数字模拟:

rosslerDiscreto = {
  x[n+1] == x[n] - C[1]*(y[n] + z[n]),
  y[n+1] == (1 - a*C[2])*y[n] + C[2]*x[n],
  z[n+1] == (z[n]*(1 - C[3]) + b*C[3]) / (1 - C[3]*x[n]),
  x[0] == y[0] == z[0] == 0.5
} /. {a->0.432, b->2, c->4, C[1]->0.1, C[2]->0.1, C[3]->0.1};
coords = RecurrenceTable[rosslerDiscreto, {x,y,z}, {n,0,1000}];
Graphics3D@Point[coords]