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Initial-switched boosting bifurcations in 2D hyperchaotic map. (English) Zbl 1445.37028
Summary: Recently, the coexistence of initial-boosting attractors in continuous-time systems has been attracting more attention. How do you implement the coexistence of initial-boosting attractors in a discrete-time map? To address this issue, this paper proposes a novel two-dimensional (2D) hyperchaotic map with a simple algebraic structure. The 2D hyperchaotic map has two special cases of line and no fixed points. The parameter-dependent and initial-boosting bifurcations for these two cases of line and no fixed points are investigated by employing several numerical methods. The simulated results indicate that complex dynamical behaviors including hyperchaos, chaos, and period are closely related to the control parameter and initial conditions. Particularly, the boosting bifurcations of the 2D hyperchaotic map are switched by one of its initial conditions. The distinct property allows the dynamic amplitudes of hyperchaotic/chaotic sequences to be controlled by switching the initial condition, which is especially suitable for chaos-based engineering applications. Besides, a microcontroller-based hardware platform is developed to confirm the generation of initial-switched boosting hyperchaos/chaos.
©2020 American Institute of Physics

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G35 Dynamical aspects of attractors and their bifurcations
37N35 Dynamical systems in control
39A33 Chaotic behavior of solutions of difference equations
Full Text: DOI
[1] Ma, J.; Wu, F. Q.; Ren, G. D.; Tang, J., A class of initials-dependent dynamical systems, Appl. Math. Comput., 298, 65-76 (2017) · Zbl 1411.37035
[2] Pisarchik, A. N.; Feudel, U., Control of multistability, Phys. Rep., 540, 4, 167-218 (2014) · Zbl 1357.34105
[3] Sharma, P. R.; Shrimali, M. D.; Prasad, A.; Kuznetsov, N. V.; Leonov, G. A., Control of multistability in hidden attractors, Eur. Phys. J. Spec. Top., 224, 1485-1491 (2015)
[4] Li, C. B.; Sprott, J. C.; Hu, W.; Xu, Y. J., Infinite multistability in a self-reproducing chaotic system, Int. J. Bifurcat. Chaos, 27, 10, 1750160 (2017) · Zbl 1383.37026
[5] Zhou, W.; Wang, G. Y.; Shen, Y. R.; Yuan, F.; Yu, S. M., Hidden coexisting attractors in a chaotic system without equilibrium point, Int. J. Bifurcat. Chaos, 28, 10, 1830033 (2018) · Zbl 1401.34022
[6] Pham, V. T.; Volos, C.; Jafari, S.; Kapitaniak, T., Coexistence of hidden chaotic attractors in a novel no-equilibrium system, Nonlinear Dyn., 87, 3, 2001-2010 (2017)
[7] Ojoniyi, O. S.; Njah, A. N., A 5D hyperchaotic Sprott B system with coexisting hidden attractors, Chaos Solitons Fractals, 87, 172-181 (2016) · Zbl 1355.34071
[8] Kengne, J.; Tabekoueng, Z. N.; Tamba, V. K.; Negou, A. N., Periodicity, chaos, and multiple attractors in a memristor-based Shinriki’s circuit, Chaos, 25, 10, 103126 (2015) · Zbl 1374.94910
[9] Stankevich, N.; Volkov, E., Multistability in a three-dimensional oscillator: Tori, resonant cycles and chaos, Nonlinear Dyn., 94, 4, 2455-2467 (2018)
[10] Bao, B. C.; Li, Q. D.; Wang, N.; Xu, Q., Multistability in Chua’s circuit with two stable node-foci, Chaos, 26, 4, 043111 (2016)
[11] Bao, H.; Liu, W. B.; Chen, M., Hidden extreme multistability and dimensionality reduction analysis for an improved non-autonomous memristive FitzHugh-Nagumo circuit, Nonlinear Dyn., 96, 3, 1879-1894 (2019)
[12] Chen, C. J.; Chen, J. Q.; Bao, H.; Chen, M.; Bao, B. C., Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons, Nonlinear Dyn., 95, 4, 3385-3399 (2019)
[13] Rajagopal, K.; Munoz-Pacheco, J. M.; Pham, V. T.; Hoang, D. V.; Alsaadi, F. E.; Alsaadi, F. E., A Hopfield neural network with multiple attractors and its FPGA design, Eur. Phys. J. Spec. Top., 227, 7-9, 811-820 (2018)
[14] Bao, H.; Liu, W. B.; Hu, A. H., Coexisting multiple firing patterns in two adjacent neurons coupled by memristive electromagnetic induction, Nonlinear Dyn., 95, 1, 43-56 (2019)
[15] Bao, B. C.; Hu, A. H.; Bao, H.; Xu, Q.; Chen, M.; Wu, H. G., Three-dimensional memristive Hindmarsh-Rose neuron model with hidden coexisting asymmetric behaviors, Complexity, 2018, 3872573
[16] Ngouonkadi, E. B. M.; Fotsin, H. B.; Fotso, P. L.; Tamba, V. K.; Cerdeira, H. A., Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator, Chaos Solitons Fractals, 85, 151-163 (2016) · Zbl 1355.34078
[17] Pisarchik, A. N.; Jaimes-Reátegui, R.; García-Vellisca, M. A., Asymmetry in electrical coupling between neurons alters multistable firing behavior, Chaos, 28, 033605 (2018)
[18] Bao, H.; Wang, N.; Bao, B. C.; Chen, M.; Jin, P. P.; Wang, G. Y., Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria, Commun. Nonlinear Sci. Numer. Simul., 57, 264-275 (2018)
[19] Bao, B. C.; Jiang, T.; Wang, G. Y.; Jin, P. P.; Bao, H.; Chen, M., Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability, Nonlinear Dyn., 89, 2, 1157-1171 (2017)
[20] Chen, M.; Sun, M. X.; Bao, B. C.; Wu, H. G.; Xu, Q.; Wang, J., Controlling extreme multistability of memristor emulator-based dynamical circuit in flux-charge domain, Nonlinear Dyn., 91, 2, 1395-1412 (2018)
[21] Chen, M.; Sun, M.; Bao, H.; Hu, Y.; Bao, B., Flux-charge analysis of two-memristor-based Chua’s circuit: Dimensionality decreasing model for detecting extreme multistability, IEEE Trans. Ind. Electron., 67, 3, 2197-2206 (2020)
[22] Jafari, S.; Pham, V. T.; Golpayegani, S. M. R. H.; Moghtadaei, M.; Kingni, S. T., The relationship between chaotic maps and some chaotic systems with hidden attractors, Int. J. Bifurcat. Chaos, 26, 13, 1650211 (2016) · Zbl 1354.37044
[23] Zhang, X.; Chen, G. R., Polynomial maps with hidden complex dynamics, Discrete Continuous Dyn. Syst. Ser. B, 24, 6, 2941-2954 (2019) · Zbl 1429.37011
[24] Munir, F. A.; Zia, M.; Mahmood, H., Designing multi-dimensional logistic map with fixed-point finite precision, Nonlinear Dyn., 97, 2147-2158 (2019) · Zbl 1430.68094
[25] Alawida, M.; Samsudin, A.; Teh, J. S.; Alshoura, W. H., Deterministic chaotic finite-state automata, Nonlinear Dyn., 98, 2403-2421 (2019) · Zbl 1430.37040
[26] Panahi, S.; Sprott, J. C.; Jafari, S., Two simplest quadratic chaotic maps without equilibrium, Int. J. Bifurcat. Chaos, 28, 12, 1850144 (2018) · Zbl 1404.34020
[27] Pisarchik, A. N.; Goswami, B. K., Annihilation of one of the coexisting attractors in a bistable system, Phys. Rev. Lett., 84, 7, 1423-1426 (2000)
[28] Sausedo-Solorio, J. M.; Pisarchik, A. N., Dynamics of unidirectionally coupled bistable Hénon maps, Phys. Lett. A, 375, 42, 3677-3681 (2011) · Zbl 1252.37027
[29] Martins, L. C.; Gallas, J. A. C., Multistability, phase diagrams and statistical properties of the kicked rotor: A map with many coexisting attractors, Int. J. Bifurcat. Chaos, 18, 6, 1705-1717 (2008)
[30] Natiq, H.; Banerjee, S.; Ariffin, M. R. K.; Said, M. R. M., Can hyperchaotic maps with high complexity produce multistability?, Chaos, 29, 011103 (2019) · Zbl 1406.94075
[31] Singh, T. U.; Nandi, A.; Ramaswamy, R., Coexisting attractors in periodically modulated logistic maps, Phys. Rev. E, 77, 6, 066217 (2008)
[32] Patra, M., Multiple attractor bifurcation in three-dimensional piecewise linear maps, Int. J. Bifurcat. Chaos, 28, 10, 1830032 (2018) · Zbl 1401.37059
[33] Richter, H., On a family of maps with multiple chaotic attractors, Chaos Solitons Fractals, 36, 3, 559-571 (2008) · Zbl 1142.37029
[34] Zhusubaliyev, Z. T.; Mosekilde, E., Multistability and hidden attractors in a multilevel DC/DC converter, Math. Comput. Simul., 109, 32-45 (2015)
[35] Zhusubaliyev, Z. T.; Mosekilde, E.; Pavlova, E. V., Multistability and torus reconstruction in a DC-DC converter with multilevel control, IEEE Trans. Ind. Inform., 9, 4, 1937-1946 (2013)
[36] Zhang, X.; Bao, B. C.; Bao, H.; Wu, Z. M.; Hu, Y. H., Bi-stability phenomenon in constant on-time controlled buck converter with small output capacitor ESR, IEEE Access, 6, 1, 46227-46232 (2018)
[37] Hegedűs, F.; Lauterborn, W.; Parlitz, U.; Mettin, R., Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving, Nonlinear Dyn., 94, 1, 273-293 (2018)
[38] Yadav, K.; Prasad, A.; Shrimali, M. D., Control of coexisting attractors via temporal feedback, Phys. Lett. A, 382, 32, 2127-2132 (2018) · Zbl 1404.34077
[39] Wang, Z.; Akgul, A.; Pham, V. T.; Jafari, S., Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors, Nonlinear Dyn., 89, 3, 1877-1887 (2017)
[40] Lai, Q.; Norouzi, B.; Liu, F., Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors, Chaos Solitons Fractals, 114, 230-245 (2018) · Zbl 1415.34079
[41] Peng, G. Y.; Min, F. H., Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit, Nonlinear Dyn., 90, 3, 1607-1625 (2017)
[42] Bao, B. C.; Xu, Q.; Bao, H.; Chen, M., Extreme multistability in a memristive circuit, Electron. Lett., 52, 1008-1010 (2016)
[43] Li, C. B.; Sprott, J. C.; Mei, Y., An infinite 2-D lattice of strange attractors, Nonlinear Dyn., 89, 4, 2629-2639 (2017)
[44] Li, C. B.; Sprott, J. C., An infinite 3-D quasiperiodic lattice of chaotic attractors, Phys. Lett. A, 382, 8, 581-587 (2018) · Zbl 1383.35031
[45] Sun, J. W.; Zhao, X. T.; Fang, J.; Wang, Y. F., Autonomous memristor chaotic systems of infinite chaotic attractors and circuitry realization, Nonlinear Dyn., 94, 4, 2879-2887 (2018)
[46] Li, C. B.; Xu, Y. J.; Chen, G. R.; Liu, Y. J.; Zheng, J. C., Conditional symmetry: Bond for attractor growing, Nonlinear Dyn., 95, 2, 1245-1256 (2019)
[47] Lai, Q.; Chen, C. Y.; Zhao, X. W.; Kengne, J.; Volos, C., Constructing chaotic system with multiple coexisting attractors, IEEE Access, 7, 24051-24056 (2019)
[48] Chen, M.; Ren, X.; Wu, H. G.; Xu, Q.; Bao, B. C., Periodically varied initial offset boosting behaviors in a memristive system with cosine memductance, Front. Inf. Technol. Electron. Eng., 20, 12, 1706-1716 (2019)
[49] Chen, M.; Ren, X.; Wu, H. G.; Xu, Q.; Bao, B. C., Interpreting initial offset boosting via reconstitution in integral domain, Chaos Solitons Fractals, 131, 109544 (2019)
[50] Bao, H.; Chen, M.; Wu, H. G.; Bao, B. C., Memristor initial-boosted coexisting plane bifurcations and its extreme multi-stability reconstitution in two-memristor-based dynamical system, Sci. China Technol. Sci. (2019)
[51] Buscarino, A.; Fortuna, L.; Patanè, L., Master-slave synchronization of hyperchaotic systems through a linear dynamic coupling, Phys. Rev. E, 100, 3, 032215 (2019)
[52] Frederickson, P.; Kaplan, J. L.; Yorke, E. D.; Yorke, J. A., The Liapunov dimension of strange attractors, J. Differ. Equ., 49, 2, 185-207 (1983) · Zbl 0515.34040
[53] Bandt, C.; Pompe, B., Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett., 88, 17, 174102 (2002)
[54] He, S. B.; Sun, K. H.; Banerjee, S., Dynamical properties and complexity in fractional-order diffusionless Lorenz system, Eur. Phys. J. Plus, 131, 8, 254 (2016)
[55] Hua, Z. Y.; Zhou, Y. C.; Bao, B. C., Two-dimensional sine chaotification system with hardware implementation, IEEE Trans. Ind. Inform., 16, 2, 887-897 (2020)
[56] Wang, N.; Li, C. Q.; Bao, H.; Chen, M.; Bao, B. C., Generating multi-scroll Chua’s attractors via simplified piecewise-linear Chua’s diode, IEEE Trans. Circuits Syst. I, 66, 12, 4767-4779 (2019)
[57] Li, C. Q.; Feng, B. B.; Li, S. J.; Kurths, J.; Chen, G. R., Dynamic analysis of digital chaotic maps via state-mapping networks, IEEE Trans. Circuits Syst. I, 66, 6, 2322-2335 (2019)
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