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Paras31

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9 Badges

2 years, 81 days
Agricultural University of Athens
PhD Candidate

Social Networks and Content at Maplesoft.com

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Teacher of Mathematics with a proven track record of working in education management. Proficient in Ease of Adaptation, Course Design, and Instructional Technology. Holds a Bachelor's degree in Mathematics from the University of the Aegean and a Master's in Applied Mathematics at the Hellenic Open University, focusing on Ordinary and Partial Differential Equations. His enthusiasm lies in the application of mathematical models to real-world contexts, such as epidemiology and population growth. Aside from his passion for teaching, Athanasios enjoys football, basketball, and spending time with his dogs.

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These are questions asked by Paras31

Maple Ambassador Portal...

Paras31 240 Maple
education portal documentation
August 23 2024
1 1

Hello community,

I recently became a Maple Ambassador and  I would like to ask about some portals that were mentioned to me. Are these portals on mapleprimes and how can I access them?

I was thinking that I could also create a LinkedIn group, so that I could present there the activities I will do at the university, the online workshops I will do in the future or upload material from student projects.

Best Regards,

Athanasios Paraskevopoulos

Duffing equation : Transition to Chaos...

Paras31 240 Maple 2024
ode odeplot differential-equations
August 22 2024
2 9

Studying the attached document, Duffing Equation from the University of Colorado, I tried to plot the Duffing equation in three different ways. My worksheet is attached.
But I didn't get the desired result as you can see below. Any suggestion on how to fix my problem?

 

Download Example.mw

 

Plotting equilibrium points...

Paras31 240 Maple 2024
ode differential-equations plotting
August 21 2024
1 21

I am preparing some examples to start the year in the differential equations lesson. And I was wondering if there is any other way to represent the equilibrium points than the following which I found and then plotted using pointplot.

restart

NULL

alpha := 0.4e-1; beta := 0.8e-2; sys := {diff(g(t), t) = -.25*g(t)+beta*p(t)*g(t), diff(p(t), t) = .7*p(t)*(1-(1/100)*p(t))-alpha*p(t)*g(t)}; ics := {g(0) = 5, p(0) = 20}
 

sol := dsolve(`union`(sys, ics), {g(t), p(t)}, numeric, range = 0 .. 50); with(plots); plots:-display(plots:-odeplot(sol, [t, p(t)], 0 .. 50, color = blue, legend = ["p(t)"]), plots:-odeplot(sol, [t, g(t)], 0 .. 50, color = red, legend = ["gt)"]), labels = ["t", "Population"], title = "Population Dynamics")

  

eqns := {.7*p(t)*(1-(1/100)*p(t))-alpha*p(t)*g(t) = 0, -.25*g(t)+beta*p(t)*g(t) = 0}; eq_points := solve(eqns, {g(t), p(t)}); eq_points

{g(t) = 0., p(t) = 0.}, {g(t) = 0., p(t) = 100.}, {g(t) = 12.03125000, p(t) = 31.25000000}

 (1)

eqpoints := pointplot([[0, 0], [100, 0], [31.25000000, 12.03125000]], color = [red], symbol = diamond, symbolsize = 15)

``
phaseplot := odeplot(sol, [p(t), g(t)], 0 .. 35, color = green, thickness = 2)

with(DEtools); vectorfield_plot := dfieldplot([diff(p(t), t) = .7*p(t)*(1-(1/100)*p(t))-alpha*p(t)*g(t), diff(g(t), t) = -.25*g(t)+beta*p(t)*g(t)], [p(t), g(t)], t = 0 .. 35, p = 0 .. 150, g = 0 .. 30, arrows = small, color = blue, axes = boxed)

 

 

display([vectorfield_plot, phaseplot, eqpoints])

  

NULL


 

Download aquarium.mw

Rossler Attractor with animations...

Paras31 240 Maple 2024
animation differential-equations rossler
August 12 2024
1 0

I was looking at the application center about attractors and found the Rossler attractor app that illustrates the Rossler Attractor with animations, as you can see below. But when I try to run it on my laptop  the two last plots remain empty. Why is this happening?

Rossler Flow System - Rossler Attractor

by Yufang Hao, <yhao@student.math.uwaterloo.ca>

This worksheet contains the images of the Rossler Attractor and the animations that follow the trajectory.

> 

restart; with(DEtools): with(plots):

Warning, the name changecoords has been redefined

  

The Rossler attractor is defined by a set of three Differential equations:

x' = -(y+z)

y' = x+a*y

z' = b + x*z - c*z

where the coefficients a, b, and c are adjustable constants.

> 

rosslerEqns := [
diff(x(t),t) = -(y(t)+z(t)),
diff(y(t),t) = x(t) + a*y(t),
diff(z(t),t) = b + x(t)*z(t) - c*z(t) ];

rosslerEqns := [diff(x(t), t) = -y(t)-z(t), diff(y(t), t) = x(t)+a*y(t), diff(z(t), t) = b+x(t)*z(t)-c*z(t)]

 (1)
> 

a:=0.17: b:=0.4: c:=8.5:
DEplot3d(rosslerEqns, {x(t),y(t),z(t)}, t=0..300,
         [[x(0)=0, y(0)=0, z(0)=0]],
         x =-15..15, y=-15..15,z=-5..25,
         stepsize=0.05, linecolour=1+sin(t*Pi/3)/2,
         thickness=1, orientation = [-110,71]);

 
> 

a:=0.17: b:=0.4: c:=8.5:
display(
  [seq(
    DEplot3d(rosslerEqns, {x(t),y(t),z(t)}, t=0..4*i,
         [[x(0)=0, y(0)=0, z(0)=0]],
         x =-15..15, y=-15..15,z=-5..25,
         stepsize=0.05, linecolour=1+sin((i-t)*Pi/5)/2,
         thickness=2, orientation = [-110,71]),
    i=1..25) # end seq
  ], # end DEplot3d list
insequence=true);

 
> 

a:=0.17: b:=0.4: c:=8.5:
display(
  [seq(
    DEplot3d(rosslerEqns, {x(t),y(t),z(t)}, t=0..4*i,
         [[x(0)=0, y(0)=0, z(0)=0]],
         x =-15..15, y=-15..15,z=-5..25,
         stepsize=0.05, linecolour=1+sin((i-t)*Pi/5)/2,
         thickness=2, orientation = [-110,71]),
    i=1..25) # end seq
  ], # end DEplot3d list
insequence=true);

 
> 

 

> 

 

> 

 


 

Download rossler_attractor.mws

Seeking Recommendations for an Ebook on ...

Paras31 240 Maple
ebook dynamical-systems
August 07 2024
0 2

I'm looking for a comprehensive ebook on mathematical modeling, specificaly focused on dynamical systems and how to use Maple for simulations and analysis. Does anyone have any recommendations for a good resource or textbook that covers these topics thoroughly?

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