In this paper, we propose a novel fourth-order memristive chaotic system (MCS), in which both its dynamical behaviors and the preassigned-time stabilization problem are analyzed. First, the dynamical behaviors of the proposed MCS are studied in detail, such as the infinite unstable equilibrium points, the chaotic attractor, the Lyapunov exponents, the Kaplan–Yorke dimension, and the bifurcation. Then, the T–S fuzzy method is employed to characterize the MCS, and a simpler model is built to deal with the nonlinearity caused by the memristor in the MCS. In addition, two intermittent controllers are proposed to guarantee the preassigned-time stability and the settling time, which can be set freely, independent of system parameters and initial state. Finally, numerical simulations provide solid confirmation for the validity of these theoretical results.
REFERENCES
1.
E. N.
Lorenz
, “Deterministic nonperiodic flow
,” J. Atmos. Sci.
20
(2
), 130
–141
(1963
). 2.
C.
Bonatto
, J. A. C.
Gallas
, and Y.
Ueda
, “Chaotic phase similarities and recurrences in a damped-driven Duffing oscillator
,” Phys. Rev. E
77
(2
), 026217
(2008
). 3.
C.
Bonatto
and J. A. C.
Gallas
, “Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit
,” Phys. Rev. Lett.
101
(5
), 054101
(2008
). 4.
C.
Rupa
, M.
Harshitha
, G.
Srivastava
, T. R.
Gadekallu
, and P. K. R.
Maddikunta
, “Securing multimedia using a deep learning based chaotic logistic map
,” IEEE J. Biomed. Health Inf.
27
(3
), 1154
–1162
(2023
). 5.
R.
Gallas
, R.
Gallas
, and J. A. C.
Gallas
, “Distribution of chaos and periodic spikes in a three-cell population model of cancer
,” Eur. Phys. J.: Spec. Top.
223
(11
), 2131
–2144
(2014
).6.
W.
Jing
, M.
Zhen
, H.
Guan
, W.
Luo
, and X.
Liu
, “A prediction model for building energy consumption in a shopping mall based on chaos theory
,” Energy Rep.
8
, 5303
–5312
(2023
).7.
Sukono
, A.
Sambas
, S.
He
, H.
Liu
, S.
Vaidyanathan
, Y.
Hidayat
, and J.
Saputra
, “Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system
,” Adv. Contin. Discrete Models
2020
, 674
(2020
).8.
L.
Wang
, Y.
Zhou
, X.
Da
, and Q.
Lai
, “Fixed-/Preassigned-time stability control of chaotic power systems
,” Inter. J. Bifurcat. Chaos
33
(9
), 2350110
(2023
). 9.
R.
Tchitnga
, T.
Nguazon
, P. H.
Louodop Fotso
, and J. A. C.
Gallas
, “Chaos in a single op-amp-based jerk circuit: Experiments and simulations
,” IEEE Trans. Circuits Syst. II: Express Briefs
63
(3
), 239
–243
(2016
).10.
F.
Yuan
, S.
Li
, Y.
Deng
, Y.
Li
, and G.
Chen
, “Cu-doped
nanoscale memristive applications in chaotic circuit and true random number generator
,” IEEE Trans. Ind. Electron.
70
(4
), 4120
–4127
(2023
). 11.
Q.
Lai
, Z.
Wan
, L. K.
Kengne
, P. D. K.
Kuate
, and C.
Chen
, “Two-memristor-based chaotic system with infinite coexisting attractors
,” IEEE Trans. Circuits Syst. II: Express Briefs
68
(6
), 2197
–2201
(2021
).12.
J.
Wu
, C.
Li
, X.
Ma
, T.
Lei
, and G.
Chen
, “Simplification of chaotic circuits with quadratic nonlinearity
,” IEEE Trans. Circuits Syst. II: Express Briefs
69
(3
), 1837
–1841
(2022
).13.
L.
Chua
, “Memristor—The missing circuit element
,” IEEE Trans. Circuit Theory
18
(5
), 507
–519
(1971
). 14.
D. B.
Strukov
, G. S.
Snider
, D. R.
Stewart
, and R. S.
Williams
, “The missing memristor found
,” Nature
453
(7191
), 80
–83
(2008
). 15.
L.
Wang
, H.
He
, and Z.
Zeng
, “Global synchronization of fuzzy memristive neural networks with discrete and distributed delays
,” IEEE Trans. Fuzzy Syst.
28
(9
), 2022
–2034
(2020
). 16.
G.
Cao
, C.
Gao
, J.
Wang
, J.
Lan
, and X.
Yan
, “Memristor based on two-dimensional titania nanosheets for multi-level storage and information processing
,” Nano Res.
15
, 8419
–8427
(2022
). 17.
M.
Ma
, Y.
Yang
, Z.
Qiu
, Y.
Peng
, Y.
Sun
, Z.
Li
, and M.
Wang
, “A locally active discrete memristor model and its application in a hyperchaotic map
,” Nonlinear Dyn.
107
, 2935
–2949
(2022
). 18.
H.
Kim
, M. P.
Sah
, C.
Yang
, S.
Cho
, and L. O.
Chua
, “Memristor emulator for memristor circuit applications
,” IEEE Trans. Circuits Syst. I: Regular Papers
59
(10
), 2422
–2431
(2012
).19.
M.
Messadi
, K.
Kemih
, L.
Moysis
, and C.
Volos
, “A new 4D memristor chaotic system: Analysis and implementation
,” Integration
88
, 91
–100
(2023
). 20.
H.
Bao
, H.
Li
, Z.
Hua
, Q.
Xu
, and B.
Bao
, “Sine-transform-based memristive hyperchaotic model with hardware implementation
,” IEEE Trans. Indus. Inf.
19
(3
), 2792
–2801
(2023
). 21.
N.
Semenova
and D.
Brunner
, “Impact of white noise in artificial neural networks trained for classification: Performance and noise mitigation strategies
,” Chaos
34
(5
), 051101
(2024
). 22.
T.
Takagi
and M.
Sugeno
, “Fuzzy identification of systems and its applications to modeling and control
,” IEEE Trans. Syst., Man, Cybern.
SMC-15
(1
), 116
–132
(1985
). 23.
H.
Xia
, J.
Tang
, W.
Yu
, C.
Cui
, and J.
Qiao
, “Takagi-Sugeno fuzzy regression trees with application to complex industrial modeling
,” IEEE Trans. Fuzzy Syst.
31
(7
), 2210
–2224
(2023
). 24.
S. H.
Tsai
and Y. W.
Chen
, “A novel interval type-2 fuzzy system identification method based on the modified fuzzy C-regression model
,” IEEE Trans. Cybern.
52
(9
), 9834
–9845
(2022
). 25.
C.
Liang
, M.
Ge
, Z. W.
Liu
, X.
Zhan
, and J. H.
Park
, “Predefined-time stabilization of T-S fuzzy systems: A novel integral sliding mode-based approach
,” IEEE Trans. Fuzzy Syst.
30
(10
), 4423
–4433
(2022
). 26.
Q.
Chang
, J. H.
Park
, Y.
Yang
, and F.
Wang
, “Finite-time multiparty synchronization of T-S fuzzy coupled memristive neural networks with optimal event-triggered control
,” IEEE Trans. Fuzzy Syst.
31
(8
), 2545
–2555
(2023
). 27.
R.
Wang
, C.
Li
, S.
Kong
, Y.
Jiang
, and T.
Lei
, “A 3D memristive chaotic system with conditional symmetry
,” Chaos Soliton. Fract.
158
, 112040
(2022
).28.
Y.
Peng
, S.
He
, and K.
Sun
, “Parameter identification for discrete memristive chaotic map using adaptive differential evolution algorithm
,” Nonlinear Dyn.
107
, 1263
–1275
(2022
). 29.
H.
Dong
, J.
Cao
, and H.
Liu
, “Observers-based event-triggered adaptive fuzzy backstepping synchronization of uncertain fractional order chaotic systems
,” Chaos
33
(4
), 043113
(2023
). 30.
S.
Yan
, J.
Song
, Y.
Cui
, L.
Li
, and J.
Wang
, “A memristive chaotic system and its application in weak signal detection
,” Phys. Scr.
98
, 105216
(2023
).31.
X.
Zhang
, C.
Li
, and H.
Li
, “Finite-time stabilization of nonlinear systems via impulsive control with state-dependent delay
,” J. Franklin Inst.
359
(3
), 1196
–1214
(2022
). 32.
L.
Wang
, S.
Jiang
, M.
Ge
, C.
Hu
, and J.
Hu
, “Finite-/Fixed-time synchronization of memristor chaotic systems and image encryption application
,” IEEE Trans. Circuits Syst. I: Regular Papers
68
(12
), 4957
–4969
(2021
). 33.
H.
Tian
, Z.
Wang
, H.
Zhang
, Z.
Cao
, and P.
Zhang
, “Dynamical analysis and fixed-time synchronization of a chaotic system with hidden attractor and a line equilibrium
,” Eur. Phys. J.: Spec. Top.
231
, 2455
–2466
(2022
). 34.
Y.
Wang
, J.
Lu
, T.
Huang
, J.
Cao
, and J.
Zhong
, “Fixed-time synchronization for two-dimensional coupled reaction-diffusion complex networks: Boundary conditions analysis
,” Chaos
34
(4
), 043116
(2024
). 35.
X.
Hu
, L.
Wang
, C.
Zhang
, X.
Wan
, and Y.
He
, “Fixed-time stabilization of discontinuous spatiotemporal neural networks with time-varying coefficients via aperiodically switching control
,” Sci. China Inform. Sci.
66
(5
), 152204
(2023
). 36.
H.
Li
, C.
Hu
, G.
Zhang
, J.
Hu
, and L.
Wang
, “Fixed-/Preassigned-time stabilization of delayed memristive neural networks
,” Inf. Sci.
610
, 624
–636
(2022
). 37.
Y.
Pan
, W.
Ji
, and H.
Liang
, “Adaptive predefined-time control for Lü chaotic systems via backstepping approach
,” IEEE Trans. Circuits Syst. II: Express Briefs
69
(12
), 5064
–5068
(2022
).38.
Z.
Cai
, L.
Huang
, and Z.
Wang
, “Fixed/Preassigned-time stability of time-varying nonlinear system with discontinuity: Application to Chua’s circuit
,” IEEE Trans. Circuits Syst. II: Express Briefs
69
(6
), 2987
–2991
(2022
).39.
Q.
Gan
, L.
Li
, J.
Yang
, Y.
Qin
, and M.
Meng
, “Improved results on fixed-/preassigned-time synchronization for memristive complex-valued neural networks
,” IEEE Trans. Neural Networks Learn. Syst.
33
(10
), 5542
–5556
(2022
). 40.
M.
Itho
and L. O.
Chua
, “Memristor oscillators
,” Inter. J. Bifurcat. Chaos
18
(11
), 3183-3296
(2008
).41.
W.
Wan
, R.
Kubendran
, C.
Schaefer
et al., “A compute-in-memory chip based on resistive random-access memory
,” Nature
608
, 504
–512
(2022
). 42.
C.
Hu
, H.
He
, and H.
Jiang
, “Fixed/Preassigned-time synchronization of complex networks via improving fixed-time stability
,” IEEE Trans. Cybern.
51
(6
), 2882
–2892
(2021
). 43.
A. K.
Pal
, S.
Kamal
, S. K.
Nagar
, B.
Bandyopadhyay
, and L.
Fridman
, “Design of controllers with arbitrary convergence time
,” Automatica
112
, 108710
(2020
). 44.
Z.
Chen
, X.
Ju
, Z.
Wang
, and Q.
Li
, “The prescribed time sliding mode control for attitude tracking of spacecraft
,” Asian J. Control
24
(4
), 1650
–1662
(2022
). 45.
Y. C.
Lai
and T.
Tél
, Transient Chaos: Complex Dynamics on Finite Time Scales
(Springer Science & Business Media
, 2011
).46.
C. K.
Volos
, V. T.
Pham
, H. E.
Nistazakis
, and I. N.
Stouboulos
, “A dream that has come true: Chaos from a nonlinear circuit with a real memristor
,” Inter. J. Bifurcat. Chaos
30
(13
), 2030036
(2020
). © 2025 Author(s). Published under an exclusive license by AIP Publishing.
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