The model contains 4 state variables *x,y,z,w*, and seven parameter
values, * c _{1},c_{2},,a,b,,A(mp)*.

The model equations are given below.

```
x' = y
```

```
y' = - x - (c
```

_{1} + c_{2}(x - y)^{2})y + aw +
bz

```
z' = z - w - A(z
```

^{2} + w^{2})z

```
w' = z + w - A(z
```

^{2} + w^{2})w

` `

To focus our investigation of this model, 5 parameter values were fixed,
at:

parameter | value |
---|---|

c_{2} | 3 |

0.3 | |

a | 3 |

b | 0 |

A | 1 |

The two remaining parameters are varied to observe the behavior of the system.

The equations for *x* and *y* are coupled together. *x*
and *y* also depend upon the values of *z* and *w*.
*z* and *w* only depend on each other. *z* and *w*
can be decoupled from the first two equations. Using polar coordinates,
the asymptotic solutions for *z(t)* and *w(t)* are given by

*z(t)* = 0,

*w(t)* = 0 when < or = 0;

*z(t)* = ,

*w(t)* = when is >
0.

where is a phase angle that depends on the
initial conditions of *z* and *w*.

Michelle Vadeboncoeur <mrvahs@wpi.edu>

Forest Lee-Elkin <yusuf@wpi.edu>