Anyone who thinks there's a huge amount of money being spent on consciousness research in AI has been badly misinformed by someone. I know only two AI researchers who claim to have implemented conscious systems, and I regard both as over-interpreting what they have done. There may be some others, but they make up a tiny minority. I have nothing against dynamical systems. Everything that changes is a dynamical system.
Computers are dynamical systems, so is the planetary system.
Some dynamical systems are well represented as collections of partial differential equations. It may be accurate for a certain level of description, e.g. it may be important for computer hardware engineers concerned with timing, stability, reliability, power consumption, etc. But it will probably not be very useful if you are either trying to design a new improved word processing packge, or if you are trying to understand a typical modern computer running most current software on most current operating systems. Those are different kinds of dynamical systems. Of course a brain is a dynamical system.