The underlying differential equation for this very minimal model is a non-dimensional version of the equation for an RC circuit, with charge measured in units of C*emf, and time measured in units of RC.
Clone of Charging a capacitor - Non-dimensional model
S-Curve + Delay for Bell Curve Showing Erlang Distribution
Generation of Bell Curve from Initial Market through Delay in Pickup of Customers
This provides the beginning of an Erlang distribution model
The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:
- a positive integer 'shape'
- a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.
Clone of S-Curve + Delay for Bell Curve by Guy Lakeman
Bipolar II treatment modeling using Van der Pol-like oscillators.
In this simulation an afflicted individual with Bipolar II disorder is put to treatment after 20 months the calibration of the medicine or treatment he recieves is such that it simulates the natural cycles of a "normal being". You can note by manipulating the parameters that sometimes too much treatment disrupts equilibria. Also note that in the state diagrams there are 2 limit cycles, the lower one being the healthiest as there are less changes.
Bipolar II dynamics
Z207 from Hartmut Bossel System Zoo 1 p103-107
After running the default settings Bossel describes A=0.2, B=0.2, Initial Values X=0 Y=2 and Z=0 and varying C=2,3,4,5 shows period doubling and transition to chaotic behavior
Rossler Chaotic Attractor
LAM Emanuel Apostol. Esperimento 3
In diesem Modell wird das Verhalten, also die Positionsänderungen von drei Körpern innerhalb eines Bezugssystems aufgrund der Gravitationskraft simuliert. Je nach Änderung der Parameter (Masse, Ausgangsposition, Radius der Massen(-punkte) variiert auch die Chaotizität des System.
Zusätzlich wird als Gedankenexperiment die Reibungskraft die durch ein hypothetisches umgebenes Medium entsteht eingeführt und die Auswirkung auf die Chaotizität gezeigt.
Clone of 3-Körper-Problem mit Reibung
OVERSHOOT GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION
The existing global capitalistic growth paradigm is totally flawed
The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks
See Guy Lakeman Bubble Theory for more details on keeping systems within finite limited size working capacity containers (villages communities)
Clone of OVERSHOOT GROWTH INTO TURBULENCE
A Fourier series is a way to expand a periodic function in terms of sines and cosines. The Fourier series is named after Joseph Fourier, who introduced the series as he solved for a mathematical way to describe how heat transfers in a metal plate.
The GIFs above show the 8-term Fourier series approximations of the square wave and the sawtooth wave.
Fourier series
Spring-Mass model used in IACS physics class
Clone of Spring-Mass Model
D'après l'article Wikipedia
Oscillateur de Van der Pol
Clone of Wind Resistance Model
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency.
The oscillator is driven with a force that is a sine function of time, with a frequency that can be varied, expressed as a forcing ratio driving frequency/natural frequency.
An accurate solution requires a small time step and RK4 as the integration algorithm.
Clone of Driven damped oscillator
Z207 from Hartmut Bossel System Zoo 1 p103-107
After running the default settings Bossel describes A=0.2, B=0.2, Initial Values X=0 Y=2 and Z=0 and varying C=2,3,4,5 shows period doubling and transition to chaotic behavior
Clone of Rossler Chaotic Attractor
S-Curve + Delay for Bell Curve Showing Erlang Distribution
Generation of Bell Curve from Initial Market through Delay in Pickup of Customers
This provides the beginning of an Erlang distribution model
The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:
- a positive integer 'shape'
- a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.
Clone of S-Curve + Delay for Bell Curve by Guy Lakeman
Spring-Mass model used in IACS physics class
Clone of Spring-Mass Model
Simulate an impact of an asteroid of any Diameter at any given Speed!
Clone of Asteroid impact simulator
In diesem Modell wird das Verhalten, also die Positionsänderungen von drei Körpern innerhalb eines Bezugssystems aufgrund der Gravitationskraft simuliert. Je nach Änderung der Parameter (Masse, Ausgangsposition, Radius der Massen(-punkte) variiert auch die Chaotizität des System.
Zusätzlich wird als Gedankenexperiment die Reibungskraft die durch ein hypothetisches umgebenes Medium entsteht eingeführt und die Auswirkung auf die Chaotizität gezeigt.
Clone of 3-Körper-Problem mit Reibung
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency.
The oscillator is driven with a force that is a sine function of time, with a frequency that can be varied, expressed as a forcing ratio driving frequency/natural frequency.
An accurate solution requires a small time step and RK4 as the integration algorithm.
Driven damped oscillator
THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION
The existing global capitalistic growth paradigm is totally flawed
Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)
The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks
See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)
Clone of THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES CHAOTIC TURBULENCE (+controls)
FORCED GROWTH GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION
BEWARE pushing increased growth blows the system!
(governments are trying to push growth on already unstable systems !)
The existing global capitalistic growth paradigm is totally flawed
The chaotic turbulence is the result of the concept and flawed strategy of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks
See Guy Lakeman Bubble Theory for more details on keeping systems within finite limited size working capacity containers (villages communities)
Clone of FORCED GROWTH INTO TURBULENCE
This model shows the different forces that influences a skier speed
Clone of Clone of Speed of a skier during a turn with a defined radius
