Abstract
Although many chaotic systems already exist, the construction methods for multi-scroll/multi-wing switching chaotic systems with general applicability are rare. This research proposes an efficient chaotic system construction method that is capable of producing multi-scroll/multi-wing switching chaotic systems with general applicability, and has theoretical and engineering feasibility. A simple method for generating self-excited attractors with multiple scrolls/wings is presented, and the range of general parameters is given. Taking Liu’s chaotic system as an experimental case, the chaotic properties of the newly developed multi-wing switched system are validated and confirmed. The multi-wing chaotic system exhibits strong multi-stability, and interesting phenomena of attractor separation are observed when offset boost is added to the linear term or the order and function of the nonlinear term are changed. Finally, the chaotic circuit is constructed, which can generate high-quality chaotic signals with good experimental results.
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References
Ai W, Sun K, Fu Y (2018) Design of multiwing-multiscroll grid compound chaotic system and its circuit implementation. Int J Mod Phys C 29(06):1850049
Chang D, Li ZJ, Wang MJ, Zeng YC (2018) A novel digital programmable multi-scroll chaotic system and its application in FPGA-based audio secure communication. AEU-INT J Electron C 88:20–29
Chen L, Pan W, Wu R, Machado JAT, Lopes AM (2016) Design and implementation of grid multi-scroll fractional-order chaotic attractors. Chaos Interdiscip J Nonlinear Sci 26:84303
Chen L, Pan W, Wu R, Wang K, He Y (2016) Generation and circuit implementation of fractional-order multi-scroll attractors, Chaos. Solitons Fract 85:22–31
Chen G, Tetsushi U (1999) Yet another chaotic attractor. Int J Bifurcat Chaos 9(07):1465–1466
Chen Z, Wen GL, Zhou HA, Chen JY (2017) A new M \(\times\) N-grid double-scroll chaotic attractors from Rucklidge chaotic system. Optik 136:27–35
Chen Z, Wen G, Zhou H, Chen J (2017) Generation of gridmulti-scroll chaotic attractors via hyperbolic tangent function series. Opt Int J Light Elect Opt 130:594–600
Chen LP, Wu RC, Chu ZB, He YG (2016) Stabilization of fractional-order coupled systems with time delay on networks. Nonlinear Dyn 88(1):1–8
Fritzkowski P, Awrejcewicz J (2021) Near-resonant dynamics, period doubling and chaos of a 3-DOF vibro-impact system. Nonlinear Dynam 106:81–103
Gilardi-Velázquez Héctor E, Escalante-González Rodolfo J, Campos Eric (2020) Emergence of a square chaotic attractor through the collision of heteroclinic orbits. Eur Phys J-Spec Top 229(6–7):1351–1360
Gu J, Li C, Chen Y, Iu HHC, Lei T (2020) A conditional symmetric memristive system with infinitely many chaotic attractors. IEEE Access 8:12394–12401
Gu ZY, Li CB, Herbert HCI, Min FH, Zhao YB (2019) Constructing hyperchaotic attractors of conditional symmetry. Eur Phys J B 92(10):221
Günay E, Altun K (2018) Multi-scroll chaotic attractors in SC-CNN via hyperbolic tangent function. Electronics 7(5):67
Han F, Hu J, Yu X, Wang Y (2007) Fingerprint images encryption via multi-scroll chaotic attractors. Appl Math Comput 185(2):931–939
Hong Q, Li Y, Wang X, Zeng Z (2018) A versatile pulse control method to generate arbitrary multidirection multibutterfly chaotic attractors. IEEE T Comput Aid D 38(8):1480–1492
Hong Q, Xie Q, Xiao P (2017) A novel approach for generating multi-direction multi-double-scroll attractors. Nonlinear Dynam 87(2):1015–1030
Hu XY, Liu CX, Liu L, Yao YP, Zhen GC (2017) Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system. Chin Phys B 26(11):110502
Kengne J, Njikam SM, Signing VRF (2018) A plethora of coexisting strange attractors in a simple jerk system with hyperbolic tangent nonlinearity. Chaos Soliton Fract 106:201–213
Lai Q, Kuate P, Pei H, Fotsin H (2020) Infinitely many coexisting attractors in no-equilibrium chaotic system. Complexity 2020:1–17
Li C, Thio JC, Sprott JC, Iu HHC, Xu Y (2018) Constructing infinitely many attractors in a programmable chaotic circuit. IEEE Access 6:29003–29012
Li Y, Li Z, Ma M, Wang MG (2020) Generation of grid multi-wing chaotic attractors and its application in video secure communication system. Multimed Tools Appl 79:29161–29177
Liu CX, Liu T, Liu K, Liu L (2004) A new chaotic attractor, Chaos. Solitons Fract 22(5):1031–1039
Lorenz Edward N (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141
Lü J, Chen G (2002) A new chaotic attractor coined. Int J Bifurcat Chaos 12(03):659–661
Ma JP, Wang LD, Duan SK, Wu JL (2016) Design of a tensile-type 3-D multi-scroll chaotic system and its application in secure communication. IEEE J Sel Areas Commun 37(12):142–155
Mohanty NP, Dey R, Roy BK (2018) A new 3-D memristive time-delay chaotic system with multi-scroll and hidden attractors. IFAC-PapersOnLine 51(1):580–585
Muñoz-Pacheco JM, Guevara-Flores DK, Félix-Beltrán OG, Tlelo-Cuautle E, Barradas-Guevara JE, Volos CK (2018) Experimental verification of optimized multiscroll chaotic oscillators based on irregular saturated functions. Complexity 2018:1–17
Pano-Azucena AD, Jose RM, Tlelo-Cuautle E (2017) Arduino-based chaotic secure communication system using multi-directional multi-scroll chaotic oscillators. Nonlinear Dyn 87(4):1–15
Rajagopal K, Cicek S, Naseradinmousavi P, Khalaf AJM, Jafari S, Karthikeyan A (2018) A novel parametrically controlled multi-scroll chaotic attractor along with electronic circuit design. Eur Phys J Plus 133(9):354
Solak E, Rhouma R, Belghith S (2010) Cryptanalysis of a multi-chaotic systems based image cryptosystem. Opt Commun 283(2):232–236
Soliman NS, Tolba MF, Said LA, Madian AH, Radwan AG (2019) Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software. Chaos Solitons Fract 126:292–307
Sun JY, Li CB, Lu TN, Akgul A, Min FH (2020) A memristive chaotic system with hypermultistability and its application in image encryption. IEEE Access 99:1–1
Swathy PS, Thamilmaran K (2014) Hyperchaos in SC-CNN based modified canonical Chua’s Circuit. Nonlinear Dyn 78(4):2639–2650
Wang N, Li C, Bao H, Bao B (2019) Generating multi-scroll Chua’s attractors via simplified piecewise-linear Chua’s diode. IEEE T CIRCUITS-I 66(12):4767–4779
Wang C, Liu X, Xia H (2017) Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N+1-scroll chaotic attractors system. Chaos 27(3):033114
Wu RC, Lu Y, Chen LP (2015) Finite-time stability of fractional delayed neural networks. Neurocomputing 149:700–707
Yan M, Jie F (2022) Fractional-order multiwing switchable chaotic system with a wide range of parameters. Chaos Solitons Fract 160:112161
Yan M, Xu H (2021) The multi-scroll hyper-chaotic coexistence attractors and its application. Signal Process-Image 95:116210
Ye X, Wang X, Gao S, Mou J, Wang Z (2020) A new random diffusion algorithm based on the multi-scroll Chua’s chaotic circuit system. Opt Laser Eng 127:105905
Zhang GT, Wang FQ (2018) A novel multi-scroll chaotic generator: Analysis, simulation, and implementation. Chin Phys B 27(1):018201
Zhang GT, Wang FQ (2018) A novel multi-scroll chaotic generator: analysis, simulation, and implementation. Chin Phys B 27(1):5
Zhang CX, Yu SM (2016) A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control. Chin Phys B 25(5):050503
Zhang S, Zeng YC, Li ZJ (2018) A novel four-dimensional no-equilibrium hyper-chaotic system with grid multiwing hyper-chaotic hidden attractors. J Comput 13(9):090908
Zhang S, Zeng Y, Li Z, Wang M, Xiong L (2018) A novel grid multiwing chaotic system with only non-hyperbolic equilibria. Pramana 90(5):1–9
Zhou L, You Z, Tang Y (2021) A new chaotic system with nested coexisting multiple attractors and riddled basins. Chaos Solitons Fract 148:111057
Acknowledgements
This work was supported by China-Northern Macedonia intergovernmental scientific and technological cooperation project (Grant No.[2019]22:6-8);Scientific research project of Education Department of Liaoning Province (Grant No.LJKMZ20220779); Natural Science Foundation of Liaoning Province (Grant No.2022-BS-211).
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Yan, M., Zhang, P. & Jie, J. A Simple Construction Method of Multi-stable Switched Multi-scroll/Multi-wing Chaotic System and Circuit Design. Iran J Sci Technol Trans Electr Eng 48, 103–114 (2024). https://doi.org/10.1007/s40998-023-00656-z
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DOI: https://doi.org/10.1007/s40998-023-00656-z