Nonlinear dynamics Definition and 29 Threads

I want to show the boundedness of the nonlinear system below. Assume, ##N, P, K, t > 0## and all other parameters to be positive. $$\frac{{d}N}{{d}t} ~=~ rN\left(1 - \frac{N}{K}\right) - \frac{a(1 - m)NP}{1 + \gamma(1 - m)N}$$ $$\frac{{d}P}{{d}t} ~=~ \frac{b(1 - m)NP}{1 + \gamma(1 - m)N} -...

What are the remaining open problems and challenges of nonlinear dynamics and chaos?

Hi, my name is Vini. I am Graduated in Physics. I worked as a visiting researcher at the Institute of Complex Systems (ISC) at the National Research Council (Consiglio Nazionale Delle Ricerche) in Florence, Italy. My research interests are differential geometry, statistical mechanics, and...

I was dealing with nonlinear systems of differential equations like the Lorenz equations (https://en.wikipedia.org/wiki/Lorenz_system). Now there is a trapping region of this system defined by the ellipsoid ρx^2+σy^2+σ(z-2ρ)^2<R. I wondered how this region is found and I found out that a...

This thread is a direct shoot-off of this post from the thread Atiyah's arithmetic physics. Manasson V. 2008, Are Particles Self-Organized Systems? The author convincingly demonstrates that practically everything known about particle physics, including the SM itself, can be derived from first...

I think that the existence of subharmonics is also bifurcation.Is that true

Chaos is when the waveforms become aperiodic. I think bifurcation is the phenomenon inclusive of chaos and in addition, it is also termed for situations in which the waveforms become n-periodic.Does bifurcation include period-n phenomenon as well as chaos? From period-n it means that still the...

Why is chaos only more studied in dc-dc converters and not in other nonlinear circuits, such as, rectifiers?

The term 'phase space' is often used in the study of nonlinear dynamics.What is it.

In state space, the coordinates are the state variables of a system.So,each point in state space represents a specific value of state variables.Thus,state space representation represents the changes in a dynamical system. The state variables are the minimum number of variables which uniquely...

Chaos is deterministic behavior.Why is chaos deterministic.Why chaos is not random. Chaos is sensitive dependence on initial conditions,a slight change in initial condition can give rise to totally different trajectories.

In my rough understanding Molecular Dynamics using Classical Newtonian mechanics is a 6N dimensional non linear system. 6N dimension because you have 3 position vectors and 3 momentum vectors for each N particles. Nonlinearity because of the terms in force fields. In principle this system can...

What would be the best book for me if I want to learn nonlinear dynamics ? I have my basics clear in linear differential equations, linear system theory, integral transforms and random process if they suffice as prerequisites.

Here is the table of contents of Nonlinear Dynamics and Chaos (by Strogatz) Overview Flows on the Line Bifurcations Flows on the Circle Linear Systems Phase Plane Limit Cycles Bifurcations Revisited Lorenz Equations One-Dimensional Maps Fractals Strange Attractors Last quarter, there was a...

Hi all, I'm a ME graduate student concentrating in fluids and I'm trying to decide between two electives. The two I'm looking at are Nonlinear Control Systems or Advanced Heat Transfer. Nonlinear controls looks interesting, but I'm not sure how it could tie in with fluids...as opposed to heat...

I want to investigate the phenomenon of Chaos in the form of how its driving amplitude affects _____, in a driven, damped pendulum, using a computer simulation given. Initially I was looking at 'degree of chaos' for the dependent variable - to measure this I wanted to use the Lyapunov...

What textbooks would you recommend for self studying Nonlinear Dynamics? I am a undergraduate junior who will be doing research on nonlinearity of spiking neurons. I have taken courses on ODE, vector calculus, probability, statistics, and linear algebra.

I completed the book 'Nonlinear Dynamics and Chaos' by Strogatz. What will be next good book to learn about nonlinear dynamics?

Homework Statement a) Find a mechanical system that is approximately governed by \dot{x}=sin(x) b) Using your physical intuition, explain why it now becomes obvious that x*=0 is an unstable fixed point and x*=\pi is stable. Homework Equations \dot{x}=sin(x) (?) The Attempt at a Solution...

Strogatz's Nonlinear and Dynamics book states that $$ \langle\sin^{2n}\rangle = \frac{1\cdot 3\cdot 5\cdots (2n-1)}{2\cdot 4\cdot 6\cdots 2n} $$ for $n\geq 1$. However, $\langle\sin^6\rangle = \frac{5}{16}\neq\frac{15}{48}$. What is the deal here?

Show that all vector fields on the line are gradient systems. This is exercise 7.2.4 in the book "Nonlinear Dynamics and Chaos" by Steven H.Strogatz Thanks very much!

Practice Problems to "Nonlinear Dynamics..." Strogatz Book Hi, I'm taking a dynamics course which uses the "nonlinear dynamics and chaos" book by Strogatz. I get a half-descent understanding from the lectures of the prof and the book's explanations of things, but \ is\ there\ a\ good\...

Homework Statement Consider the system x' + x = F(t), where F is smooth, T-periodic function. IS it true that the system necessarily has a stable T-periodic solution x(t)? If so, Prove it; If not, find an F that provides a counterexample. Homework Equations x' + x = F(t) The...

Basically where are nonlinear dynamics and chaos theory used in the real world? Like if someone studies it what type of areas might they find it being useful for? The only example I can seem to think of is stuff like weather/fluids/air resistance/physics. What might be some other more...

Homework Statement Find the fixed points and classify them using linear analysis. Then sketch the nullclines, the vector field, and a plausible phase portrait. dx/dt = x(x-y), dy/dt = y(2x-y) Homework Equations The Attempt at a Solution f1(x,y) = x(x-y) x-nullcline: x(x-y) = 0 \Rightarrow...

Hi everyone, I am studying a 2-D nonlinear dynamics system, with two key parameters. But I have trouble when I want to locate where the homoclinic bifurcation occurs in the parameter space. Can anyone give me some ideas or reference readings? Thx

First off, though I've been reading through these forums for a while now, this is my first post here, so let me briefly introduce myself. I'm finishing up my third year as an undergraduate in mathematics. Next year, I want to apply to grad school in math, specifically, I'd like to study...

I'm interested in focusing on nonlinear dynamics or mathematical physics for my PhD and was wondering if anyone could tell me what US universities have strong departments in these topics. I've heard that Cornell is good for dynamics and chaos but haven't heard much about other colleges. Thanks.

I recently came across [FONT=Comic Sans MS]Nonlinear Dynamics and Chaos by Strogatz and I'm recommending it to all my Physics/Applied Math friends. This is a great introductory book on the subject and you don't need any more Math than is taught in a basic Diff. Eq. course. I love this book...