I am having a system of differential equations as follows, now this is a non-linear system -
$\dot{x}(t) = -0.28571(x + f_{1}) + 0.00057(g_{1} - z) $
$\dot{y}(t) = \frac{1}{c_{2}}(-2.4*y + 0.000101*f_{1}*y + 2.4*g_{2} -c_{2}*\dot{h_{1}} - 0.000101*h_{1}*x - 0.006*x)$
$\dot{z}(t) = -\dot{g_{1}} - \frac{f_{1}}{c_{1}}(0.0000113*g_{1} + 0.0072) - \frac{z}{c_{1}}(-0.0000113*x + 2.4) - \frac{f_{1}.z}{c_{1}}(0.0000741) + \frac{y}{c_{1}}(2.4) + 19.6*c_{3} + \frac{1}{c_{1}}(2.4*h_{1} - 2.4*g_{1} + 0.0000741*g_{1}*x + 0.0072*x)$.
Where $f_{1},g_{1},g_{2},h_{1}$ are continuous functions of time $t$ ,$c_{1},c_{2},c_{3}$ are the constants .
Now I am interested in the functions $f_{1},g_{1},g_{2},h_{1}$ and constants $c_{1},c_{2},c_{3}$ so that chaotic dynamics may occur , like I had selected these values Initial values - $x(0) = -10000 , y(0) = 100 , z(0) = 4 , c_{1} = 10 ,c_{2} = 10 , c_{3} = 101$, Due to physical constraint $x$ has to take negative values.
I got the phase space as something like this -
Actally I am interested to explore this system with some interesting properties it might have, also it may appear little clumsy and sophisticated.
Also this doesnot appear to be chaotic , any speciality in this system of ODE one can observe and is Chaotic behaviour possible here?
Like any method we can use so as to study these system of Non linear ODE's so that we can extract dynamical behaviour from the system.
$EDIT$
$x(t)$ represents the initial velocity of the wind from ocean to land surface.
$f_{2}$ represents the velocity of the wind above the land surface which is usually zero but I am taking it as a function of time to generalize the phenomena.
$g_{1}(t)$ represents the initial temperature at the land-ocean interface.
$z(t)$ represents the temperature at the land surface.
$h_{1}$ is the initial moisture content at the land-ocean interface.
$y(t)$ represents the moisture content at the land surface.
$c_{1},c_{2},c_{4}$ are the constants
Actually I am mainly interested in the following - Like which specific functions should I choose in order to get a Chaotic behaviour and does this system seem to generate some interesting dynamics like for a choice of functions and constants?
Any help is great!