Table 2 Lyapunov characteristics exponents of dynamical system (6) for various values of \(\alpha \).
From: A physical memristor based Muthuswamy–Chua–Ginoux system
m | LCE spectrum | Dynamics of the attractor | Hausdorff dimension |
|---|---|---|---|
\(0.001< \alpha < 0.08\) | \((0, 0, -)\) | 2-Torus | \(D = 2\) |
\(0.08< \alpha < 0.1\) | \((0, -, -)\) | \(1-\)Periodic motion (limit cycle) | \(D = 1\) |
\(0.11< \alpha < 0.13\) | \((+, 0, -)\) | Spiral-chaos | \(D = 2.18\) |
\(0.14< \alpha < 0.19\) | \((0, -, -)\) | n-Periodic motion | \(D = 1\) |
\(\alpha = 0.20\) | \((+, 0, -)\) | Spiral-chaos | \(D = 2.14\) |
\(0.21< \alpha < 0.23\) | \((0, -, -)\) | n-Periodic motion | \(D = 1\) |
\(0.24< \alpha < 0.28\) | \((0, -, -)\) | \(1-\)Periodic motion (limit cycle) | \(D = 1\) |
\(0.29< \alpha < 0.30\) | \((0, -, -)\) | n-Periodic motion | \(D = 1\) |
\(0.30< \alpha < 0.98\) | \((+, 0, -)\) | Spiral-chaos | \(D = 2.21\) |
\(1< \alpha < 1.1\) | \((0, -, -)\) | \(1-\)Periodic motion (limit cycle) | \(D = 1\) |
\(1.2< \alpha < 2.9\) | \((+, 0, -)\) | Double spiral-chaos | \(D = 2.19\) |
