• Chinese Physics B
  • Vol. 29, Issue 10, (2020)
Peng-Fei Ding1,2, Xiao-Yi Feng1,†, and Cheng-Mao Wu2
Author Affiliations
  • 1School of Electronics and Information, Northwestern Polytechnical University, Xi’an 70072, China
  • 2School of Electronics and Engineering, Xi’an University of Posts and Telecommunications, Xi’an 71011, China
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    DOI: 10.1088/1674-1056/ab9dea Cite this Article
    Peng-Fei Ding, Xiao-Yi Feng, Cheng-Mao Wu. Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system[J]. Chinese Physics B, 2020, 29(10): Copy Citation Text show less
    The waveform of the different sine functions: (a) f(x) with b = 0.5 and n1 = n2 = 2, (b) g(x) with b = 0.5, (c) h(x) with A = 6 and a = 0.5 π, (d) p(x) with a = 1, b = 0.1, c = 3, and d = 0. The a, c, and d are real constants, and x, y, and z are state variables of the system (3). The b, n1, and n2 are real constants in Eq. (4). The number of scrolls generated by the system (3) with suitable parameters can be adjusted by the parameters n1 and n2.
    Fig. 1. The waveform of the different sine functions: (a) f(x) with b = 0.5 and n1 = n2 = 2, (b) g(x) with b = 0.5, (c) h(x) with A = 6 and a = 0.5 π, (d) p(x) with a = 1, b = 0.1, c = 3, and d = 0. The a, c, and d are real constants, and x, y, and z are state variables of the system (3). The b, n1, and n2 are real constants in Eq. (4). The number of scrolls generated by the system (3) with suitable parameters can be adjusted by the parameters n1 and n2.
    Different number of scroll chaotic attractors are generated by system (3) with a = c = d = 0.3 and b = 0.5: (a) 3-scroll chaotic attractor with n1 = 1 and n2 = 2, (b) 5-scroll chaotic attractor with n1 = 2 and n2 = 3.
    Fig. 2. Different number of scroll chaotic attractors are generated by system (3) with a = c = d = 0.3 and b = 0.5: (a) 3-scroll chaotic attractor with n1 = 1 and n2 = 2, (b) 5-scroll chaotic attractor with n1 = 2 and n2 = 3.
    Grid multi-scroll chaotic attractors for a = 1, b = 0.5, c = 0.3, d = 0.5, and A = 1: (a) 6 × 3 grid multi-scroll chaotic attractors with n1 = 3, n2 = 3, and M = 1; (b) 5 × 4 grid multi-scroll chaotic attractors with n1 = 2, n2 = 3, and M = 2.
    Fig. 3. Grid multi-scroll chaotic attractors for a = 1, b = 0.5, c = 0.3, d = 0.5, and A = 1: (a) 6 × 3 grid multi-scroll chaotic attractors with n1 = 3, n2 = 3, and M = 1; (b) 5 × 4 grid multi-scroll chaotic attractors with n1 = 2, n2 = 3, and M = 2.
    The equilibrium point distribution of the 6 × 3 grid multi-scroll chaotic attractors.
    Fig. 4. The equilibrium point distribution of the 6 × 3 grid multi-scroll chaotic attractors.
    The system (9) with Eqs. (4) and (10), and d ∈ (0,1): (a) Lyapunov exponents; (b) bifurcation diagram.
    Fig. 5. The system (9) with Eqs. (4) and (10), and d ∈ (0,1): (a) Lyapunov exponents; (b) bifurcation diagram.
    The specific form of the sine function f(x) with b = 0.5, n1 = n2 = 3. (a) Electronic circuit diagram; (b) simulation result with the unit of horizontal ordinate 2 s/Div, and the unit of vertical ordinate 500 mV/Div.
    Fig. 6. The specific form of the sine function f(x) with b = 0.5, n1 = n2 = 3. (a) Electronic circuit diagram; (b) simulation result with the unit of horizontal ordinate 2 s/Div, and the unit of vertical ordinate 500 mV/Div.
    The specific form of the sine function f(x) with b = 0.5, n1 = 2, n2 = 3. (a) Electronic circuit diagram; (b) simulation result with the unit of horizontal ordinate 2 s/Div, and the unit of vertical ordinate 500 mV/Div.
    Fig. 7. The specific form of the sine function f(x) with b = 0.5, n1 = 2, n2 = 3. (a) Electronic circuit diagram; (b) simulation result with the unit of horizontal ordinate 2 s/Div, and the unit of vertical ordinate 500 mV/Div.
    The sign function f1(y) of Eq. (10) with A = 1, M = 1. (a) Electronic circuit diagram; (b) circuit simulation result with the unit of horizontal ordinate 1 V/Div, and the unit of vertical ordinate 1 V/Div.
    Fig. 8. The sign function f1(y) of Eq. (10) with A = 1, M = 1. (a) Electronic circuit diagram; (b) circuit simulation result with the unit of horizontal ordinate 1 V/Div, and the unit of vertical ordinate 1 V/Div.
    The sign function f1(y) of Eq. (11) with A = 1, M = 1. (a) Electronic circuit diagram; (b) circuit simulation result with the unit of horizontal ordinate 1 V/Div, and the unit of vertical ordinate 2 V/Div.
    Fig. 9. The sign function f1(y) of Eq. (11) with A = 1, M = 1. (a) Electronic circuit diagram; (b) circuit simulation result with the unit of horizontal ordinate 1 V/Div, and the unit of vertical ordinate 2 V/Div.
    Grid multi-scroll chaotic attractor circuit.
    Fig. 10. Grid multi-scroll chaotic attractor circuit.
    Circuit simulation results: (a) 6 × 3 grid multi-scroll chaotic attractors, (b) 5 × 4 grid multi-scroll chaotic attractors.
    Fig. 11. Circuit simulation results: (a) 6 × 3 grid multi-scroll chaotic attractors, (b) 5 × 4 grid multi-scroll chaotic attractors.
    Hardware circuits experimental results. (a) Hardware circuits connection diagram; (b) experimental results of the 6 × 3 grid multi-scroll chaotic attractors; (c) experimental results of the 5 × 4 grid multi-scroll chaotic attractors.
    Fig. 12. Hardware circuits experimental results. (a) Hardware circuits connection diagram; (b) experimental results of the 6 × 3 grid multi-scroll chaotic attractors; (c) experimental results of the 5 × 4 grid multi-scroll chaotic attractors.
    Peng-Fei Ding, Xiao-Yi Feng, Cheng-Mao Wu. Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system[J]. Chinese Physics B, 2020, 29(10):
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