All Questions
Tagged with nonlinear-dynamics mathematical-modeling
11
questions
1
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1
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148
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Reaction Diffusion Equation general solution
I have been struggling to find the general solution of the following BVP of reaction-diffusion equation:
$$\frac{\partial N}{\partial t}=\frac{\partial^2 N}{\partial x^2}+N(1-N)-\sigma N$$
$$N(0,x)=...
- 11
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0
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47
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Can you modeling complicated dynamics without using differential/difference equations?
Let's imagine there is a phenomenon I want to understand. I have a few multivariate time series about the phenomenon but not a lot. I don't know how the variables are related to each other but from ...
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1
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66
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Spherical Parallel Manipulator Lagrangian problem
I faced a very serious problem and I urgently need the help of specialists in robotics, mechanics, physics and mathematics.
I am trying to derive equations of motion from the Lagrangian of a spherical ...
- 731
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35
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Which nonlinear Observer to study to estimate the speed of the Plant?
I have designed the mathematical model of the plant with nonlinear hystersis function $f(x_1)$ and is validated using simulation. Now I want to design the nonlinear observer to estimate the speed (...
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45
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Systems that Display Chaotic Behavior
I take a course in 'nonlinear dynamics and chaos'.
For our final project, we have to choose a dynamical system in that is nonlinear and specifically one that displays chaotic behavior.
I know that ...
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200
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Lyapunov Function at Fixed Point
Given the following system:
$$\frac{dx}{dt} = x\left(2-x-y\right)$$
$$\frac{dy}{dt} = x-y$$
I found fixed points $(0,0)$ and $(1,1)$. I then want to show that this function is Lyapunov for $x>0$ :...
- 125
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0
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259
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Constructing a trapping region in a 2D dynamical system
Consider a system of the form $$\frac{d}{dt}x \enspace = \enspace 2-\left(b+1\right)x + ax^2y$$ $$\frac{d}{dt}y\enspace=\enspace bx-ax^2y$$
This is the context of some homework I have. I've already ...
- 125
4
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2
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376
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What was the idea behind Logistic growth model?
The Malthus model is given by
$\frac{dP(t)}{dt}=rP(t)$, where $r$ is the growth rate. This model ignores the competition for resources among individuals. So, Verhulst came up with a model
$\frac{...
- 1,271
1
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2
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2k
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Partial differential equations that involve an infinite "continuum" of variables: "Each point in space contributes additional degrees of freedom"?
Page 11, Nonlinear Dynamics and Chaos, by Strogatz, says the following:
This is the domain of classical applied mathematics and mathematical physics where the linear partial differential equations ...
- 4,322
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2
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Improved model of a fishery: $\dot N=rN(1-\frac{N}{K})-H\frac{N}{A+N}$
Strogatz exercise $3.7.4.a:$
An improved model of a fishery is:
$$\dot N=rN\left(1-\frac{N}{K}\right)-H\frac{N}{A+N}.$$
a) Give a biological interpretation of the parameter $A$; what does it ...
- 1,123
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69
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Finite Difference Equation From a Non-Linear Equation
Given a Non-Linear Equation that is:
$$I\ddot\theta = mgl \cdot \sin \theta + F_D \cdot l + k\theta $$
Where, $$F_D$$ is representative of Drag Force and is equal to:
$$-1/2C_D\rho Av^2\cdot \...
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