This paper presents an extension of the three-dimensional Bao system by incorporating a memristor as a feedback element, thereby constructing a four-dimensional hyper-chaotic system. By analyzing the dynamic properties of the system, the study confirms the system’s complex and rich hyper-chaotic behavior. An analog circuit is designed using basic electronic components, validating the consistency between the circuit’s simulated and numerical results. Based on these findings, a novel control strategy is proposed: the monotonic width-adjustable pulse control strategy. The key innovation of this strategy lies in its ability to dynamically adjust the control width sequence in a monotonically varying manner, enhancing both the adaptability and effectiveness of the control process. The exponential stability of the strategy was rigorously verified through mathematical analysis. The effectiveness and practical applicability of the proposed control method are demonstrated by its successful stabilization of the newly developed hyper-chaotic system and its effective regulation of the respiratory disease model.
AbbaATehJAlawidaM (2024) Towards accurate keyspace analysis of chaos-based image ciphers. Multimedia Tools and Applications83(33): 79047–79066.
2.
AghababaMHashtarkhaniB (2015) Synchronization of unknown uncertain chaotic systems via adaptive control method. Journal of Computational and Nonlinear Dynamics10(5): 051004.
3.
BabanliKOrtac KabaogluR (2024) Synchronization of fuzzy-chaotic systems with z-controller in secure communication. Information Sciences657: 119988.
4.
BaoBWangNXuQ, et al. (2016) A simple third-order memristive band pass filter chaotic circuit. IEEE Transactions on Circuits and Systems II: Express Briefs64: 977–981.
5.
BaptistaM (2021) Chaos for communication. Nonlinear Dynamics105: 1821–1841.
6.
BoydSEl GhaouiLFeronE, et al. (1994) Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM.
7.
ChenHChangJYanJ, et al. (2008) EP-based PID control design for chaotic synchronization with application in secure communication. Expert Systems with Applications34: 1169–1177.
8.
ChenJYanDDuanS, et al. (2020) Memristor-based hyper-chaotic circuit for image encryption. Chinese Physics B29: 110504.
9.
ChenWXuWZhengW (2024) Sliding-mode-based impulsive control for a class of time-delay systems with input disturbance. Automatica164: 111633.
DingKZhuQ (2021) Fuzzy intermittent extended dissipative control for delayed distributed parameter systems with stochastic disturbance: a spatial point sampling approach. IEEE Transactions on Fuzzy Systems30: 1734–1749.
12.
FekiM (2009) Sliding mode control and synchronization of chaotic systems with parametric uncertainties. Chaos, Solitons & Fractals41: 1390–1400.
13.
FirthW (1991) Chaos–predicting the unpredictable. BMJ British Medical Journal303: 1565–1568.
14.
FredericksonPKaplanJYorkeE, et al. (1983) The Liapunov dimension of strange attractors. Journal of Differential Equations49: 185–207.
15.
GabelliJFèveGBerroirJ, et al. (2006) Violation of Kirchhoff’s laws for a coherent RC circuit. Science313: 499–502.
16.
GholipourYRamezaniAMolaM (2014) Illustrate the butterfly effect on the chaos Rikitake system. Universitas Ahmad Dahlan3(4): 273–276.
17.
GuE (2024) The inherent law of the unpredictability of financial asset price fluctuations: multistability and chaos. Journal of Systems Science and Complexity37: 776–804.
18.
GuoPShiQJianZ, et al. (2024) An intelligent controller of homo-structured chaotic systems under noisy conditions and applications in image encryption. Chaos, Solitons & Fractals180: 114524.
19.
HuangLSunYXiangJ, et al. (2022) Image encryption based on a novel memristive chaotic system, Grain-128a algorithm and dynamic pixel masking. Journal of Systems Engineering and Electronics33: 534–550.
20.
KhanATyagiA (2017) Analysis and hyper-chaos control of a new 4-D hyper-chaotic system by using optimal and adaptive control design. International Journal of Dynamics and Control5: 1147–1155.
21.
LaaremG (2021) A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos synchronization using optimized fractional order sliding mode control. Chaos, Solitons & Fractals152: 111437.
22.
LaiQLaiCZhangH, et al. (2022) Hidden coexisting hyperchaos of new memristive neuron model and its application in image encryption. Chaos, Solitons & Fractals158: 112017.
23.
LeaDAllenMHaineT (2000) Sensitivity analysis of the climate of a chaotic system. Tellus A: Dynamic Meteorology and Oceanography52(5): 523–532.
24.
LeeSParkMKwonO, et al. (2019) Improved synchronization criteria for chaotic neural networks with sampled-data control subject to actuator saturation. International Journal of Control Automation and Systems17: 2430–2440.
25.
LiQChenL (2024) An image encryption algorithm based on 6-dimensional hyper chaotic system and DNA encoding. Multimedia Tools and Applications83: 5351–5368.
26.
LiHMinF (2024) Large-scale memrisitive Rulkov ring-star neural network with complex spatio-temporal dynamics. IEEE Transactions on Industrial Informatics20(8): 10259–10268.
27.
LiZTaoKXiaQ, et al. (2021) Finite-time impulsive control of financial risk dynamic system with chaotic characteristics. Complexity2021(1): 5207154.
28.
LiKLiRCaoL, et al. (2023) Periodically intermittent control of memristor-based hyper-chaotic bao-like system. Mathematics11: 1264.
29.
LiuSZuoYLiT, et al. (2024) Adaptive fixed-time PID-based control of uncertain nonlinear systems and its application to unmanned surface vehicles. International Journal of Systems Science55(14): 2815–2824.
30.
LorenzEN (1963) Deterministic nonperiodic flow. Journal of the Atmospheric Sciences20: 130–141.
31.
MansourMDonmezTKutluM, et al. (2023) Respiratory diseases prediction from a novel chaotic system. Chaos Theory and Applications5(1): 20–26.
32.
MashuriAAdenanNAbd KarimNS, et al. (2024) Application of chaos theory in different fields—a literature review. Journal of Science and Mathematics Letters12: 92–101.
33.
MeiCGuoDChenG, et al. (2024) Event-triggered adaptive control for a class of nonlinear systems with dead-zone input. Electronics13: 210.
34.
MinFYinSChengY (2024) Hybrid-diode-based Shinriki circuit: coexisting oscillations and bifurcation trees. IEEE Transactions on Circuits and Systems I: Regular Papers72(2): 896–906.
35.
MobayenSMostafaeeJAlattasK, et al. (2024) A new hyperchaotic system: circuit realization, nonlinear analysis and synchronization control. Physica Scripta99: 105204.
36.
NaikRSinghU (2024) A review on applications of chaotic maps in pseudo-random number generators and encryption. Annals of Data Science11(1): 25–50.
37.
OzpolatEGultenA (2024) Synchronization and application of a novel hyperchaotic system based on adaptive observers. Applied Sciences14(3): 1311.
38.
PoincaréH (1893) Les Méthodes Nouvelles de la Mécanique Céleste. Paris: Gauthier-Villars.
39.
RamarRVaidyanathanSAkgulA, et al. (2024) A new chaotic jerk system with cubic and hyperbolic sine nonlinearities and its application to random number generation and biomedical image encryption. Scientia Iranica. doi: 10.24200/sci.2024.63254.8303.
40.
SabaghianABalochianSYaghoobiM (2020) Synchronisation of 6D hyper-chaotic system with unknown parameters in the presence of disturbance and parametric uncertainty with unknown bounds. Connection Science32: 362–383.
41.
SanchezEPerezJ (1999) Input-to-state stability (ISS) analysis for dynamic neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications46: 1395–1398.
42.
UdhayakumarKShanmugasundaramSKashkynbayevA, et al. (2023) Saturated and asymmetric saturated impulsive control synchronization of coupled delayed inertial neural networks with time-varying delays. Applied Mathematical Modelling113: 528–544.
43.
WangQHuRBloniganP (2014) Least squares shadowing sensitivity analysis of chaotic limit cycle oscillations. Journal of Computational Physics267: 210–224.
44.
WangYWangGShenY, et al. (2020) A memristor neural network using synaptic plasticity and its associative memory. Circuits, Systems, and Signal Processing39: 3496–3511.
45.
WolfASwiftJSwinneyH, et al. (1985) Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena16: 285–317.
46.
WuKOnasanyaBCaoL, et al. (2023) Impulsive control of some types of nonlinear systems using a set of uncertain control matrices. Mathematics11: 421.
47.
XiaoWMinFLiH, et al. (2024) Complex motion behavior and synchronization analysis of heterogeneous neural network. IEEE Transactions on Circuits and Systems I: Regular Papers71(12): 5618–5627.
48.
XieXWenSFengY, et al. (2022) Three-stage-impulse control of memristor-based Chen hyper-chaotic system. Mathematics10: 4560.
49.
YangXLiuYCaoJ, et al. (2020) Synchronization of coupled time-delay neural networks with mode-dependent average dwell time switching. IEEE Transactions on Neural Networks and Learning Systems31: 5483–5496.
50.
YuanFWangGWangX (2016) Extreme multistability in a memristor-based multi-scroll hyper-chaotic system. Chaos: An Interdisciplinary Journal of Nonlinear Science26: 073107.
51.
ZhangSZengYJunL (2018) A novel four-dimensional no-equilibrium hyper-chaotic system with grid multiwing hyper-chaotic hidden attractors. Journal of Computational and Nonlinear Dynamics13: 090908.
52.
ZhuSLiRFengY, et al. (2024a) Predefined-time sliding mode filtering control of memristor-based Bao hyper-chaotic system. Journal of Vibration and Control. doi: 10.1177/10775463241272821.
53.
ZhuSLuQFengY, et al. (2024b) A 4D entangled memristor hyperchaotic system and its new predefined-time sliding mode synchronization control. IEEE Access12: 145483–145495.
