Simplest Chaotic Circuit

memristance	β ( 2 x - 1)
internal state function	- i - α x + i x

system parameters

β

1.5

α

0.6

C

1

L

3

t

500

v

0

0.1

i

0

0

x

0

0.1

2D phase portrait, time domain waveform, and a 3D phase portrait

This Demonstration shows a simulation of the simplest possible chaotic circuit. It contains just three fundamental circuit elements (inductor, capacitor, and memristor) in series. Hence, it is specified by the minimum number of states (three) required for chaos: voltage across the capacitor

v

, current through the inductor

C

, and internal state of the memristor

f(x,i)

(see [1]). The system equations are

v'=

i

C

,

i'=-

1

L

(v+R(x,i)i)

,

x'=f(x,i)

, where

i

is the inductance and

x

is unknown.