R/exponential.R

In phaseR: Phase Plane Analysis of One- And Two-Dimensional Autonomous ODE Systems

#' The exponential growth model
#'
#' The derivative function of the exponential growth model, an example of a one-
#' dimensional autonomous ODE system.
#'
#' \code{exponential} evaluates the derivative of the following ODE at the point
#' \ifelse{html}{\out{(<i>t</i>, <i>y</i>)}}{\eqn{(t, y)}}:
#'
#' \ifelse{html}{\out{<i>dy</i>/<i>dt</i> = <i>&beta;y</i>.}}{
#' \deqn{\frac{dy}{dt} = \beta y.}}
#'
#' Its format is designed to be compatible with \code{\link[deSolve]{ode}} from
#' the \code{\link[deSolve]{deSolve}} package.
#'
#' @param t The value of \ifelse{html}{\out{<i>t</i>}}{\eqn{t}}, the independent
#' variable, to evaluate the derivative at. Should be a
#' \code{\link[base]{numeric}} \code{\link[base]{vector}} of
#' \code{\link[base]{length}} one.
#' @param y The value of \ifelse{html}{\out{<i>y</i>}}{\eqn{y}}, the dependent
#' variable, to evaluate the derivative at. Should be a
#' \code{\link[base]{numeric}} \code{\link[base]{vector}} of
#' \code{\link[base]{length}} one.
#' @param parameters The values of the parameters of the system. Should be a
#' \code{\link[base]{numeric}} \code{\link[base]{vector}} prescribing the value
#' of \ifelse{html}{\out{<i>&beta;</i>}}{\eqn{\beta}}.
#' @return Returns a \code{\link[base]{list}} containing the value of the
#' derivative at \ifelse{html}{\out{(<i>t</i>, <i>y</i>)}}{\eqn{(t, y)}}.
#' @author Michael J Grayling
#' @seealso \code{\link[deSolve]{ode}}
#' @export
exponential <- function(t, y, parameters) {
  list(parameters*y)
}