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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- Chinese Physics B
- Vol. 29, Issue 10, (2020)

Fig. 1. The waveform of the different sine functions: (a) f (x ) with b = 0.5 and n 1 = n 2 = 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 , n 1, and n 2 are real constants in Eq. (4 ). The number of scrolls generated by the system (3 ) with suitable parameters can be adjusted by the parameters n 1 and n 2.

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 n 1 = 1 and n 2 = 2, (b) 5-scroll chaotic attractor with n 1 = 2 and n 2 = 3.

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 n 1 = 3, n 2 = 3, and M = 1; (b) 5 × 4 grid multi-scroll chaotic attractors with n 1 = 2, n 2 = 3, and M = 2.

Fig. 4. The equilibrium point distribution of the 6 × 3 grid multi-scroll chaotic attractors.

Fig. 5. The system (9 ) with Eqs. (4 ) and (10 ), and d ∈ (0,1): (a) Lyapunov exponents; (b) bifurcation diagram.

Fig. 6. The specific form of the sine function f (x ) with b = 0.5, n 1 = n 2 = 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, n 1 = 2, n 2 = 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. 8. The sign function f 1(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. 9. The sign function f 1(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. 10. Grid multi-scroll chaotic attractor circuit.

Fig. 11. Circuit simulation results: (a) 6 × 3 grid multi-scroll chaotic attractors, (b) 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.
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