What is the mathematical definition of the Chen–Lee attractor and its parameter set?

Conditions

• The system is defined by three coupled nonlinear ordinary differential equations.
• The parameters are set to $a=5$, $b=-10$, and $c=-0.38$.

Reasoning, step by step

1. Identify the state variables $x$, $y$, and $z$ in three-dimensional space.
2. Write the first differential equation: $\frac{dx}{dt} = ax - yz$.
3. Write the second differential equation: $\frac{dy}{dt} = by + xz$.
4. Write the third differential equation: $\frac{dz}{dt} = cz + \frac{xy}{3}$.
5. Substitute the specific parameter values $a=5$, $b=-10$, and $c=-0.38$ into the equations.

Example

The video displays the system of equations: $\frac{dx}{dt} = ax - yz$, $\frac{dy}{dt} = by + xz$, $\frac{dz}{dt} = cz + \frac{xy}{3}$, with the parameters $a=5$, $b=-10$, and $c=-0.38$.

Common misconceptions

• Assuming the parameters $a$, $b$, and $c$ can be arbitrary; the specific values are required to produce the exact chaotic structure shown.
• Confusing the Chen–Lee attractor with other chaotic systems like the Lorenz attractor, which have different equations.

Watch the explanation

Explore next

• Why are multiple particles needed to demonstrate the attractor's complex spatial structure?
• What is the Chen-Lee attractor?