| Citation: |
Huijian Zhu, Weiquan Pan, Lijie Li, Jiahao Mao. CHAOTIFICATION OF A FRACTIONAL-ORDER RADIO-PHYSICAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 742-756. doi: 10.11948/20250127
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CHAOTIFICATION OF A FRACTIONAL-ORDER RADIO-PHYSICAL SYSTEM
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Abstract
Little is known about the chaosification problem in the framework of fractionalorder nonlinear systems. Employing the negative damping instability mechanism via fractional operators, this paper identifies the onset of chaos in a fractional-order radio-physical system with order lying in (1, 2). Under the specific system parameters, we find different routes to chaos from a stable focus-node, an asymptotically period-doubling cascade, and a stable quasi-periodic orbit. We further describe the complex dynamics of the system using the largest Lyapunov exponents and the bifurcation diagram. Of particular interest is the first finding that a fractional derivative can chaotize the globally stable quasi-periodic system without feedback control.
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Keywords:
- Fractional calculus /
- chaotification /
- bifurcation /
- Lyapunov exponent
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References
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Huijian Zhu, Weiquan Pan, Lijie Li, Jiahao Mao. CHAOTIFICATION OF A FRACTIONAL-ORDER RADIO-PHYSICAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 742-756. doi: 10.11948/20250127
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Figure 1.
Phase diagrams and Poincaré section
$ x=0 $ $ (\lambda, \beta, \omega_0, b, \varepsilon, k) = (-4.5, 0.02, 2\pi, 1, 4, 0.02) $ $ \alpha=1 $ $ \alpha=1.15 $ -
Figure 2.
Largest Lyapunov exponent spectrum and bifurcation diagram of system (3.3) with
$ (\lambda, \beta, \omega_0, b, \varepsilon, k) = (-4.5, 0.02, 2\pi, 1, 4, 0.02) $ $ \alpha \in [1.0254:0.0001:1.1859] $ -
Figure 3.
Phase diagrams and Poincaré section
$ x=0 $ $ (\lambda, \beta, \omega_0, b, \varepsilon, k) = (-3.8, 0.02, 2\pi, 1, 4, 0.02) $ $ \alpha=1 $ $ \alpha=1.15 $ -
Figure 4.
Largest Lyapunov exponent spectrum and bifurcation diagram of system (3.3) with
$ (\lambda, \beta, \omega_0, b, \varepsilon, k) = (-3.8, 0.02, 2\pi, 1, 4, 0.02) $ $ \alpha \in [1.0001:0.0001:1.1729] $ -
Figure 5.
Phase diagrams and Poincaré section
$ x=0 $ $ (\lambda, \beta, \omega_0, b, \varepsilon, k) = (-3.275, 0.02, 2\pi, 1, 4, 0.02) $ $ \alpha=1 $ $ \alpha=1.1 $ -
Figure 6.
Largest Lyapunov exponent spectrum and bifurcation diagram of system (3.3) with
$ (\lambda, \beta, \omega_0, b, \varepsilon, k) = (-3.275, 0.02, 2\pi, 1, 4, 0.02) $ $ \alpha \in [1.0001:0.0001:1.1665] $