[TigersEye]

Wow! that’s a great response. Thank you. If I have understood the essence of your explanation it is that ‘chaos’ (in the context you describe) is roughly synonymous with ‘instability.’ A ‘non-chaotic’ system is a relatively stable system.

[E8crossE8]

Wow! that’s a great response. Thank you.

My pleasure.

If I have understood the essence of your explanation it is that ‘chaos’ (in the context you describe) is roughly synonymous with ‘instability.’ A ‘non-chaotic’ system is a relatively stable system.

Just as is the case for the word 'chaos,' the word ‘stability’ has a very technically specific meaning in physical dynamics. Rather than using the word stability, I would prefer to say that a chaotic system exhibits exquisitely sensitive dependence on the so-called boundary conditions to the solutions of the underlying equations of motion of the system. Phyiscal systems that are not chaotic are decribed by equations of motion the solutions of which do not exhibit such extreme sensitivity to boundary conditions. (“Boundary conditions” are constraints that need to be specified in order to obtain particular solutions to differential equations – unlike algebraic equations which don’t require additional information in the form of “boundary conditions” in order to be solved.)

[ The reason I want to avoid using the word 'stability’ here is that it is entirely possible for a non-chaotic system to exhibit an "unstable" solution. As an example, one way in which a perfectly non-chaotic physical system, such as one described by linear differential equations of motion, can possess an unstable solution is if a quantity called the "potential function" (this quantity is part of the equation of motion) is what is called "unbounded from below". ]