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Tagged with differential-games ordinary-differential-equations
4
questions
4
votes
0
answers
177
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System of quadratic autonomous ODEs - convexity of the solution curve
Crossposted on MathOverflow
Problem:
For a given parameter $a>0$, consider the following autonomous system of ODEs for $(x,y,z): \mathbb R_+\to [0,1)^3$:
\begin{align*}
\dot{x}_t &= (1-x_t) (...
- 1,590
1
vote
1
answer
131
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ODE equivalent to a system of Difference Equations (Discrete to Continuous time)
Consider the following gradient-descent ascent system of equations:
$$\begin{cases}
x_{k+1} = x_{k} - \eta \nabla_{x} g(x_{k}, y_{k}) \\
y_{k+1} = y_{k} + \eta \nabla_{y} g(x_{k+1}, y_{k})
\end{...
- 313
4
votes
2
answers
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Four-Dogs Pursuit [closed]
Four dogs start at the corners of square $ABCD$ (labelled anti-clockwise). Running anti-clockwise, the dog starting at $A$ pursues the dog starting at $B$, which pursues the dog starting at $C$, which ...
- 49
23
votes
4
answers
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Does Tom catch Jerry?
Tom has Jerry backed against a wall. Tom is distance 1 away (perpendicularly). At time t=0, Jerry runs along the wall. Tom runs directly towards Jerry. Tom always runs directly towards Jerry. Tom and ...
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