What is meant by waveformWorking in strogatz nonlinear dynamics, global bifurcati

In summary, the conversation discusses the concept of "waveforms" in the context of working with nonlinear dynamics and global bifurcations. The problem presented involves considering a system with equations for r' and O', and using transformations to sketch the waveforms of x(t) and y(t). The discussion also mentions that these waveforms are representative of what one might observe experimentally for a system on the brink of an infinite-period bifurcation.
  • #1
shoescreen
15
0
What is meant by "waveform". Working in strogatz nonlinear dynamics, global bifurcati

Homework Statement



Consider the system r' = r(1-r^2), O' = m - sin(O) for m slightly greater than 2. Let x = rcos(O) and y = rsin(O). Sketch the waveforms of x(t) and y(t). (These are typical of what one might see experimentally for a system on the verge of an infinite-period bifurcation.)

Homework Equations





The Attempt at a Solution



I just have no clue what it means by waveforms. As far as i can tell, they are not mentioned anywhere else in the book (at least not prior to this question). I can transform the system into x' and y', but that doesn't seem to help, and I'm fairly certain that I'm not suppose to just solve the system, or else i get messy log terms.
 
Physics news on Phys.org
  • #2
Could anyone please explain what is meant by waveforms in this context, and perhaps how to sketch them?
 

1. What is a waveform?

A waveform is a graphical representation of the shape and amplitude of a signal over time. It is commonly used to represent sound waves, electrical signals, and other types of waves.

2. What does "working in strogatz nonlinear dynamics" mean?

Working in strogatz nonlinear dynamics refers to studying complex systems using mathematical models and analysis developed by Steven Strogatz, a renowned mathematician and physicist. This field of study focuses on understanding the behavior of nonlinear systems, which exhibit behaviors that cannot be predicted by simple linear models.

3. What is global bifurcation?

Global bifurcation is a phenomenon in nonlinear dynamics where a small change in a system's parameters can lead to a drastic change in its behavior. This can result in the appearance of new stable states or the sudden disappearance of existing ones.

4. How is global bifurcation relevant in real-world applications?

Global bifurcation has important applications in various fields, such as biology, ecology, and economics. It helps us understand how small changes in a complex system can lead to major shifts in its behavior, allowing us to make predictions and better manage these systems.

5. Can global bifurcation be controlled or manipulated?

While global bifurcation cannot be controlled directly, understanding its mechanisms and how it affects a system can help us manipulate and control the system's behavior. This is especially relevant in fields such as engineering and control theory, where predicting and controlling complex systems is crucial.

Similar threads

Dynamical Systems: how to find equation for Poincare map?
    • Calculus and Beyond Homework Help
Replies
1
Views
966
Nonlinear coordinate transformation
    • Calculus and Beyond Homework Help
Replies
1
Views
2K
Applied Nonlinear Dynamics & Chaos: Is It Possible to Jump In Mid-Book?
    • Science and Math Textbooks
Replies
1
Views
1K
Nonlinear Dynamics Strogatz(m
    • Calculus and Beyond Homework Help
Replies
1
Views
4K
Using Index Theory to show a system has no closed orbits
    • Calculus and Beyond Homework Help
Replies
1
Views
4K
Improper integral with spherical coordinates
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Dynamic Systems: Poincaré-Bendixson Theorem finite # of equilibria
    • Differential Equations
Replies
4
Views
1K
Integrating FE and Dynamics
    • Mechanical Engineering
Replies
2
Views
978
Hopf Bifurcation - Nonlinear Diff Eqns
    • Calculus and Beyond Homework Help
Replies
1
Views
2K
Nonlinear system phase portraits
    • Calculus and Beyond Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top