NonLinModelling          package:fNonlinear          R Documentation

_C_h_a_o_t_i_c _T_i_m_e _S_e_r_i_e_s _M_o_d_e_l_l_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     A collection and description of functions to  simulate different
     types of chaotic time series  maps. 

     Chaotic Time Series Maps:

       'tentSim'      Simulates data from the Tent Map,
       'henonSim'     simulates data from the Henon Map,
       'ikedaSim'     simulates data from the Ikeda Map,
       'logisticSim'  simulates data from the Logistic Map,
       'lorentzSim'   simulates data from the Lorentz Map,
       'roesslerSim'  simulates data from the Roessler Map.

_U_s_a_g_e:

     tentSim(n = 1000, n.skip = 100, parms = c(a = 2), start = runif(1), 
         doplot = FALSE)
     henonSim(n = 1000, n.skip = 100, parms = c(a = 1.4, b = 0.3), 
         start = runif(2), doplot = FALSE)
     ikedaSim(n = 1000, n.skip = 100, parms = c(a = 0.4, b = 6.0, c = 0.9), 
         start = runif(2), doplot = FALSE)
     logisticSim(n = 1000, n.skip = 100, parms = c(r = 4), start = runif(1), 
         doplot = FALSE)
     lorentzSim(times = seq(0, 40, by = 0.01), parms = c(sigma = 16, r = 45.92, 
         b = 4), start = c(-14, -13, 47), doplot = TRUE, ...)
     roesslerSim(times = seq(0, 100, by = 0.01), parms = c(a = 0.2, b = 0.2, c = 8.0),
         start = c(-1.894, -9.920, 0.0250), doplot = TRUE, ...) 

_A_r_g_u_m_e_n_t_s:

  doplot: a logical flag. Should a plot be displayed? 

n, n.skip: [henonSim][ikedaSim][logisticSim] - 
           the number of chaotic time series points to be generated and
          the  number of initial values to be skipped from the series.  

   parms: the named parameter vector characterizing the chaotic map. 

   start: the vector of start values to initiate the chaotic map. 

   times: [lorentzSim][roesslerSim] - 
           the sequence of time series points at which to generate the
          map.  

     ...: arguments to be passed. 

_V_a_l_u_e:

     [*Sim] - 
      All functions return invisible a vector of time series data.

_A_u_t_h_o_r(_s):

     Diethelm Wuertz for the Rmetrics R-port.

_R_e_f_e_r_e_n_c_e_s:

     Brock, W.A., Dechert W.D., Sheinkman J.A. (1987);  _A Test of
     Independence Based on the Correlation  Dimension_,  SSRI no. 8702,
     Department of Economics, University of  Wisconsin, Madison.

     Eckmann J.P., Oliffson Kamphorst S., Ruelle D. (1987), 
     _Recurrence plots of dynamical systems_,  Europhys. Letters 4,
     973.

     Hegger R., Kantz H., Schreiber T. (1999); _Practical
     implementation of nonlinear time series  methods: The TISEAN
     package_, CHAOS 9, 413-435.

     Kennel M.B., Brown R., Abarbanel H.D.I. (1992);  _Determining
     embedding dimension for phase-space  reconstruction using a
     geometrical construction_,  Phys. Rev. A45, 3403. 

     Rosenstein M.T., Collins J.J., De Luca C.J. (1993); _A practical
     method for calculating largest Lyapunov  exponents from small data
     sets_,  Physica D 65, 117.

_S_e_e _A_l_s_o:

     'RandomInnovations'.

_E_x_a_m_p_l_e_s:

     ## logisticSim -
        set.seed(4711)
        x = logisticSim(n = 100)  
        plot(x, main = "Logistic Map")            

