upca                 package:simecol                 R Documentation

_T_h_e _U_n_i_f_o_r_m _P_e_r_i_o_d _C_h_a_o_t_i_c _A_m_p_l_i_t_u_d_e _M_o_d_e_l

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

     'simecol' example: resource-predator-prey model, which is able to
     exhibit chaotic behaviour.

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

       data(upca)

_F_o_r_m_a_t:

     S4 object according to the 'odeModel' specification. The object
     contains the following slots:

     '_m_a_i_n' The differential equations for predator prey and resource
          with:

          '_u' resource (e.g. grassland or phosphorus),

          '_v' producer (prey),

          '_w' consumer (predator).

'_e_q_u_a_t_i_o_n_s' Two alternative (and switchable) equations for the
     functional response.

'_p_a_r_m_s' Vector with the named parameters of the model, see references
     for details.

'_t_i_m_e_s' Simulation time and integration interval.

'_i_n_i_t' Vector with start values for 'u', 'v' and 'w'.

'_s_o_l_v_e_r' Character string with the integration method.

_D_e_t_a_i_l_s:

     To see all details, please have a look into the implementation and
     the original publications.

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

     Blasius, B., Huppert, A., and Stone, L. (1999) Complex dynamics
     and phase synchronization in spatially extended ecological
     systems. _Nature_, *399* 354-359.

     Blasius, B. and Stone, L. (2000) Chaos and phase synchronization
     in ecological systems.  _International Journal of Bifurcation and
     Chaos_, *10* 2361-2380.

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

     'sim', 'parms', 'init', 'times'.

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

         data(upca)
         plot(sim(upca))

         # omit stabilizing parameter wstar
         parms(upca)["wstar"] <- 0
         plot(sim(upca))

         # change functional response from
         # Holling II (default) to Lotka-Volterra
         equations(upca)$f <- function(x, y, k) x * y
         plot(sim(upca))

