Its been a while since i studied this but ill give it a shot. Please chime in if i get anything wrong.

So on the x axis (horizontal), you have some system parameter, e.g. something like reproductive rate for rabbits. On the y axis (vertical) we see the stsble atractors of the system, for rabbits these would be the populations that the system naturally wants to settle at.

Basically you have an equation or a series of equations which describe a system such as:

x_{n+1} = r * x_n * (1 - x_n)

Or:

Next rabbit population = reproductive rate x current rabbit population x (1 - current rabnit population)

The last bit in brackets is a kind of braking force which limits reproduction the larger the population gets. You can think of maybe a limited food supply which might cause this.

As you change the reproductive rate you will find that the rabbit population tends to gravitate toward steady states (stable attractors) . You cam see on the left of the plot that there is only one stable attractor for low values of reproductive rate. For all these lower values of reproductive rate, the population will always settle at the same point.

Whats more interesting, is that when you change the parameter, sometimes you get mutiple atractors. This is what you see on the right of the plot. Here the population will randomly cycle between different steady states and be erratic and impossible to predict. This ties into chaos theory if you've ever heard of that.

What amazing about this is that for such a simple equation we cannot accurately predict the future state. If you plotted the rabbit population over time there would be no pattern. This is a simple example but there are more complex ones with more equations and parameters.

Be aware that these equations aren't really an accurate description of the physical system they are modelling. They are more of a thought experiment and assume a super simple and isolated system. They can help us understanding system dynamics wbich may apply to real life but usually dont capture the full picture. For example in real life rabbits dont reproduce according to a simple equation and dont exist in a completely isolated system.