The Roessler Attractor

Equations:

$$\begin{align}\dot{x}_{0}&=- 1.0 \cdot x_{1} - 1.0 \cdot x_{2}\\\dot{x}_{1}&=par_{0} \cdot x_{1} + x_{0}\\\dot{x}_{2}&=par_{1} + x_{2} \cdot \left(- par_{2} + x_{0}\right)\end{align}$$

Description:

A chaotic system of equations useful for modeling equilibrium in chemical reactions.

Keywords:

chaotic

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IVP 77

Class: PINLBNU

Initial conditions:

$$\begin{align}x_{0}(0)&=0.0\\x_{1}(0)&=-10.3\\x_{2}(0)&=0.03\end{align}$$

Parameters:

$$\begin{align}par_{0}&=0.2\\par_{1}&=0.2\\par_{2}&=5.7\end{align}$$

Exact Solution^*:

No exact solution provided.

[untested]

IVP 106

Class: PINLBU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ -0.0001, 0.0001\right]\\x_{1}(0)&\subset~\left[ -10.3001, -10.2999\right]\\x_{2}(0)&\subset~\left[ 0.0299, 0.0301\right]\end{align}$$

Parameters:

$$\begin{align}par_{0}&=0.2\\par_{1}&=0.2\\par_{2}&=5.7\end{align}$$

Exact Solution^*:

No exact solution provided.

[untested]

IVP 107

Class: PINLBU

Initial conditions:

$$\begin{align}x_{0}(0)&\subset~\left[ -0.2, 0.2\right]\\x_{1}(0)&\subset~\left[ -9.58095, -9.18095\right]\\x_{2}(0)&\subset~\left[ -0.1704098, 0.2295902\right]\end{align}$$

Parameters:

$$\begin{align}par_{0}&=0.2\\par_{1}&=0.2\\par_{2}&=5.7\end{align}$$

Exact Solution^*:

No exact solution provided.

[untested]

^* rounded (non-rigorously) to 5 decimal places to preserve screen real estate.

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