Dynamical systems Definition and 62 Threads

I was recently commissioned by one of my neuroscience professors to help him develop a new gameplan for possibly describing neural networks with dynamical systems theory. In his most recent paper on the subject, he used Hidden Markov Modeling to detect coherent rate patterns in populations of...

I'm doing a research project for a class in advanced differential geometry, and have chosen to cover dynamical systems. However, I've found that the relationship between dynamical systems is limited to exploring flows on manifolds in the most abstract sense. As a result, I was hoping on expand...

1. A = {[0.4 0 .2], [0.3 0.8 0.3], [0.3 0.2 0.5]}. The vector v1 = {[0.1], [0.6], [0.3]} is an eigenvector for A, and two eigenvalues are .5 and .2. Construct the solution of the Dynamical system x,k+1 = Ax,k that satisfies x,0 = (0, 0.3, 0.7) My attempt I tried to work this one out...

There is a work in history of astronomy I've been preparing for the most of the time in living memory. I can't say is it late, or due, or long, but counting from the 3 books I've seen, the one in focus of some private interest is Michael Hoskin "Cambridge Illustrated History of Astronomy"...

I am so very sorry, but I did not know where to put this thread! I would like to request any helpful links and/or tutorials relating to basic discrete dynamical systems, or any help at all! It should cover: linear one dimension difference equations; non-linear one dimension difference...

Elite program for dynamical systems? **Mathwonk Which school has an elite program for dynamical systems? I currently go to school in NY, and if possible, I would like to go to a grad school not in the Northeastern region. If I had to guess I would say: Penn State, Cornell, Stony Brook and...

Q3. Sketch the graph of B(x) Q4. Prove that B'(0)=0 Q5. Inductively prove that B^n(0)=0 for all n.Conclude that B(x) is a c infiniti function. Q6. modify B(x) to construct a C infiniti function C(x) whcih satisfies a. C(x) =0 if x is less than or equal to 0 b. C(x) =1 if x is...

Hi, can anyone help me prove the following: Show that the nonwandering set is closed and positively invariant. I always have trouble working with sets because they're so abstract. If anyone can help me, that would be great. Thanks. Definition of nonwandering set is here...

How would i solve such a question? in a system V sub(k+1) = A V sub(k) approximate Vsub(k). there is an equation V sub(k)=b1 (lambda)^k X1 but I don't know what b is

often in my differentail equations class i took last semester we frequently evaluated 2nd order systems, they could easily be calculuted in MATLAB using pplane6, however pplane6 can only solve systems of 2nd order or less, because as its name says its a phase plane, meaning it can only evaluate...

Does anyone know anything concrete about the application of nonlinear chaotic dyamical systems to psychology? I have come to find out that there is a substantial amount of research being done on this. I read some articles today where people were trying to apply this to dysfunctional families...

I've been thinking, and I've come up with a sort of Intelligent Design argument in reverse against the existence of a God. It occurs to me that perfect shapes, such as circles, squares, rectangles, right triangles, etc .. are the product of an intelligent mind. In other words it takes an...