# Gathering interest in Dynamical Systems (Bifurcation, Stable Manifolds, Hamiltonian Systems) f

• MHB
• DrWahoo
In summary, the speaker is considering writing a lecture on graduate modeling and is open to using LaTeX or PDF format for easier sharing. The suggested topics for the lecture include basic concepts of modeling, solving differential equations, finding equilibrium points, gradient fields and phase portraits, and using MATLAB code for solving initial value problems. The speaker is also open to providing examples and practice problems. Assistance and guidance are available for those interested in writing the lecture.
DrWahoo
I am in the process of writing a lecture out for my Graduate modeling class I teach. I normally don't write lectures out in LaTex or use PDF's because I write on the dry erase board, but if anyone is interested I wouldn't mind spending the time to type out some notes on the topic.

The topic would include all the title says, with problems, solutions, gradient, phase plots and MATLAB code to solve odes. Thanks, and if this is not acceptable please delete and let me know admins.

Thank you for your interest in writing a lecture on graduate modeling. We appreciate your willingness to spend time to type out notes on this topic.We suggest using LaTeX or PDFs as these are the most commonly used formats for lectures. This will make it easier to share your lecture with your students and other members of the academic community. In order to provide a comprehensive lecture, we recommend covering topics such as the basics of modelling, solving differential equations, finding equilibrium points, gradient fields and phase portraits, and MATLAB code to solve initial value problems. You may also want to include examples and practice problems to demonstrate the concepts. If you have any questions or need help getting started, please feel free to reach out to us. We are happy to provide guidance and support. Good luck!

## 1. What are dynamical systems?

Dynamical systems are mathematical models used to describe the behavior of a system over time. They involve a set of equations that represent the relationships between the variables of the system and how they change over time.

## 2. What is bifurcation in dynamical systems?

Bifurcation refers to the point at which a small change in a system's parameters or initial conditions can lead to a significant change in the behavior of the system. It is often associated with the emergence of new patterns or behaviors in the system.

## 3. What are stable manifolds in dynamical systems?

Stable manifolds are geometric objects that represent the set of points in a dynamical system that converge to a stable equilibrium point. They provide insight into the long-term behavior of a system and help to identify regions of stability and instability.

## 4. What are Hamiltonian systems?

Hamiltonian systems are a special type of dynamical system that follows Hamilton's equations, which describe the evolution of a system's state over time. They are commonly used to model physical systems such as celestial mechanics and fluid dynamics.

## 5. Why is gathering interest in dynamical systems important?

Gathering interest in dynamical systems is important because they have a wide range of applications in various fields, including physics, biology, and economics. Studying these systems can lead to a better understanding of complex phenomena and help to make predictions about their behavior. Additionally, dynamical systems theory has practical applications in engineering and control systems.

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