| Citation: |
Xinwang Liu, Javeria Ayub, Muhammad Aqeel, Umer Farooq. NONLINEAR ANALYSIS OF PLASMA DYNAMICAL CHAOTIC SYSTEM: HIDDEN MULTISTABILITY WITH CIRCUIT IMPLEMENTATION[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1514-1530. doi: 10.11948/20260025
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NONLINEAR ANALYSIS OF PLASMA DYNAMICAL CHAOTIC SYSTEM: HIDDEN MULTISTABILITY WITH CIRCUIT IMPLEMENTATION
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Abstract
In this article, we introduce hidden multistability in plasma dynamical chaotic system with coexisting hidden and self-excited attractors. Plasma is the branch of physics that is the result of nonlinear oscillation, instability, and turbulence of particle interaction and scattering waves. The multistability in the plasma dynamical chaotic system is due to the radio-frequency oscillation of an electron gas and the excitation of a radioactive oscillation of the ion-acoustic wave. The plasma dynamical chaotic system is constructed by the amplitude of these oscillations, which exhibits chaos for particular values of parameters. Hidden multistability is investigated and confirmed in the plasma dynamical chaotic system with five major analytical tools, such as parameter constraints, basin of attraction, bifurcation diagram, Lyapunov exponents, and Poincaré section. Moreover, by utilizing the Multisim we have done a circuit implementation and subsequently validated the mathematical model. The findings of this study will provide helpful insight into the plasma dynamical chaotic system in targeting multi-stability and chaos.
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Keywords:
- Hidden multistability /
- chaos /
- bifurcation /
- Poincaré map /
- basin of attraction /
- Lyapunov exponents /
- chaotic circuit
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References
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Xinwang Liu, Javeria Ayub, Muhammad Aqeel, Umer Farooq. NONLINEAR ANALYSIS OF PLASMA DYNAMICAL CHAOTIC SYSTEM: HIDDEN MULTISTABILITY WITH CIRCUIT IMPLEMENTATION[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1514-1530. doi: 10.11948/20260025
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Figure 1.
Plasma chaotic attractor with the initial condition
$ (x_{1}, x_{2}, x_{3}) = (4, 4, 1) $ $ \alpha=7 $ $ \beta = 1 $ $ \gamma = 4 $ $ x_{1}x_{2}x_{3} $ $ x_{1}x_{2} $ $ x_{1}x_{3} $ $ x_{2}x_{3} $ -
Figure 2.
Plasma chaotic attractor with the initial conditions
$ I_{0}(x_{1}, x_{2}, x_{3}) = (4, 4, 1) $ $ I_{1}(x_{1}, x_{2}, x_{3}) = (4.05, 4, 1) $ $ I_{2}(x_{1}, x_{2}, x_{3}) = (4.10, 4, 1) $ $ \alpha=7 $ $ \beta = 1 $ $ \gamma = 4 $ $ x_{1} $ $ x_{2} $ $ x_{3} $ -
Figure 3.
Parametric constraints representation of Plasma chaotic system (2.1),
$ (\alpha, \gamma) $ $ \beta=1 $ $ p_{1} $ $ p_{2} $ $ p_{3} $ $ p_{4} $ -
Figure 4.
Basin of attraction in two-dimensional cross-section
$ x_{1}x_{2}- $ $ x_{3}=3 $ $ \alpha $ $ \beta=1 $ $ \gamma=4 $ -
Figure 5.
Lyapunov exponents with the initial condition
$ (x_{1}, x_{2}, x_{3}) = (4, 4, 1) $ $ \alpha $ $ \beta=1 $ $ \gamma=4 $ -
Figure 6.
Multi-stability in subfigures of bifurcation diagram with the variation of
$ \alpha $ $ \beta=1 $ $ \gamma=4 $ $ I_{0}(x_{1}, x_{2}, x_{3}) = (0.1, 0.1, 0.1) $ $ I_{1}(x_{1}, x_{2}, x_{3}) = (-1, 0, -1) $ -
Figure 7.
(Case01:
$ 2\leq\alpha\leq4.5 $ $ \alpha=3 $ $ \beta=1 $ $ \gamma=4 $ $ x_{1}x_{2} $ -
Figure 8.
(Case02:
$ 16\leq\alpha\leq17 $ $ \alpha=16.2 $ $ \beta=1 $ $ \gamma=4 $ $ x_{1}x_{2} $ -
Figure 9.
(Case03:
$ 18\leq\alpha\leq19 $ $ \alpha=18.5 $ $ \beta=1 $ $ \gamma=4 $ $ x_{1}x_{2} $ -
Figure 10.
Circuit design of plasma dynamical chaotic system on Multisim 14.2, for
$ \beta=1 $ $ \gamma=4 $ $ \alpha=6.75 $ -
Figure 11.
Simulation results of circuit design in Figure 10, in
$ x_{1}x_{2}- $ $ \beta=1 $ $ \gamma=4 $ $ \alpha=6.75 $ -
Figure 12.
Simulation results of circuit design in Figure 10, in
$ x_{2}x_{3}- $ $ \beta=1 $ $ \gamma=4 $ $ \alpha=6.75 $ -
Figure 13.
Simulation results of circuit design in Figure 10, in
$ x_{1}x_{3}- $ $ \beta=1 $ $ \gamma=4 $ $ \alpha=6.75 $ -
Figure 14.
Simulation results of circuit design in Figure 10, in
$ x_{1}x_{2}- $ $ \beta=1 $ $ \gamma=4 $ $ \alpha=16.2 $ -
Figure 15.
Simulation results of circuit design in Figure 10, in
$ x_{1}x_{2}- $ $ \beta=1 $ $ \gamma=4 $ $ \alpha=18.5 $