example1

The value of , the independent
variable, to evaluate the derivative at. Should be a
<code><a rd-options="base" href="/link/numeric?package=phaseR&version=2.1.3&to=base" data-mini-rdoc="base::numeric">numeric</a></code> <code><a rd-options="base" href="/link/vector?package=phaseR&version=2.1.3&to=base" data-mini-rdoc="base::vector">vector</a></code> of
<code><a rd-options="base" href="/link/length?package=phaseR&version=2.1.3&to=base" data-mini-rdoc="base::length">length</a></code> one.

The value of , the dependent
variable, to evaluate the derivative at. Should be a
<code><a rd-options="base" href="/link/numeric?package=phaseR&version=2.1.3&to=base" data-mini-rdoc="base::numeric">numeric</a></code> <code><a rd-options="base" href="/link/vector?package=phaseR&version=2.1.3&to=base" data-mini-rdoc="base::vector">vector</a></code> of
<code><a rd-options="base" href="/link/length?package=phaseR&version=2.1.3&to=base" data-mini-rdoc="base::length">length</a></code> one.

The values of the parameters of the system. Not used here.

parameters

The derivative function of an example one-dimensional autonomous ODE system.

Performs a qualitative analysis of one- and two-dimensional
autonomous ordinary differential equation systems, using phase plane methods.
Programs are available to identify and classify equilibrium points, plot the
direction field, and plot trajectories for multiple initial conditions. In
the one-dimensional case, a program is also available to plot the phase
portrait. Whilst in the two-dimensional case, programs are additionally
available to plot nullclines and stable/unstable manifolds of saddle points.
Many example systems are provided for the user. For further details can be
found in Grayling (2014) <doi:10.32614/RJ-2014-023>.

Michael J Grayling

phaseR

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

Gerhard Burger

Stephen P Ellner

John M Guckenheimer

example1 function

<dl><dt>t</dt>
<dd>The value of t, the independent
variable, to evaluate the derivative at. Should be a
<code><a href="/link/numeric?package=phaseR&version=2.1.3" data-mini-rdoc="phaseR::numeric">numeric</a></code> <code><a href="/link/vector?package=phaseR&version=2.1.3" data-mini-rdoc="phaseR::vector">vector</a></code> of
<code><a href="/link/length?package=phaseR&version=2.1.3" data-mini-rdoc="phaseR::length">length</a></code> one.</dd>
<dt>y</dt>
<dd>The value of y, the dependent
variable, to evaluate the derivative at. Should be a
<code><a href="/link/numeric?package=phaseR&version=2.1.3" data-mini-rdoc="phaseR::numeric">numeric</a></code> <code><a href="/link/vector?package=phaseR&version=2.1.3" data-mini-rdoc="phaseR::vector">vector</a></code> of
<code><a href="/link/length?package=phaseR&version=2.1.3" data-mini-rdoc="phaseR::length">length</a></code> one.</dd>
<dt>parameters</dt>
<dd>The values of the parameters of the system. Not used here.</dd></dl>

Arguments

Author

Example ODE system 1 — example1

<dl>

<dt>t</dt>
<dd>The value of t, the independent
variable, to evaluate the derivative at. Should be a
<code><a href='https://rdrr.io/r/base/numeric.html'>numeric</a></code> <code><a href='https://rdrr.io/r/base/vector.html'>vector</a></code> of
<code><a href='https://rdrr.io/r/base/length.html'>length</a></code> one.</dd>


<dt>y</dt>
<dd>The value of y, the dependent
variable, to evaluate the derivative at. Should be a
<code><a href='https://rdrr.io/r/base/numeric.html'>numeric</a></code> <code><a href='https://rdrr.io/r/base/vector.html'>vector</a></code> of
<code><a href='https://rdrr.io/r/base/length.html'>length</a></code> one.</dd>


<dt>parameters</dt>
<dd>The values of the parameters of the system. Not used here.</dd>

</dl>

example1: Example ODE system 1

Description

Usage

Value

Arguments

Author

Details

See Also