×

Conditional symmetry: bond for attractor growing. (English) Zbl 1439.94108

Summary: Coexisting attractors with conditional symmetry exist in separated asymmetric basins of attraction with identical Lyapunov exponents. It is found that when a periodic function is introduced into the offset-boostable variable, infinitely many coexisting attractors may be coined. More interestingly, such coexisting attractors may be hinged together and then grow in the phase space as the time evolves without any change of the Lyapunov exponents. It is shown that, in such cases, an initial condition can be applied for selecting the starting position; consequently, the system will present a special regime of homogenous multistability. Circuit implementation based on STM32 verifies the numerical simulations and theoretical analysis.

MSC:

94C05 Analytic circuit theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D45 Attractors of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chen, M., Xu, Q., Lin, Y., Bao, B.C.: Multistability induced by two symmetric stable node-foci in modified canonical Chua’s circuit. Nonlinear Dyn. 87, 789-802 (2017) · doi:10.1007/s11071-016-3077-6
[2] Bao, B., Li, Q., Wang, N., Xu, Q.: Multistability in Chua’s circuit with two stable node-foci. Chaos 26, 043111 (2016) · doi:10.1063/1.4946813
[3] Lai, Q., Chen, S.: Research on a new 3D autonomous chaotic system with coexisting attractors. Optik 127, 3000-3004 (2016) · doi:10.1016/j.ijleo.2015.12.089
[4] Lai, Q., Chen, S.: Generating multiple chaotic attractors from Sprott B system. Int. J. Bifurc. Chaos. 26, 1650177 (2016) · Zbl 1349.34161 · doi:10.1142/S0218127416501777
[5] Li, C., Sprott, J.C., Xing, H.: Crisis in amplitude control hides in multistability. Int. J. Bifurc. Chaos. 26, 1650233 (2016) · Zbl 1357.34106 · doi:10.1142/S0218127416502333
[6] Li, C., Hu, W., Sprott, J.C., Wang, X.: Multistability in symmetric chaotic systems. Eur. Phys. J. Spec. Top. 224, 1493-1506 (2015) · doi:10.1140/epjst/e2015-02475-x
[7] Leonov, G.A., Vagaitsev, V.I., Kuznetsov, N.V.: Localization of hidden Chua’s attractors. Phys. Lett. A. 375, 2230-2233 (2011) · Zbl 1242.34102 · doi:10.1016/j.physleta.2011.04.037
[8] Jafari, S., Sprott, J.C., Nazarimehr, F.: Recent new examples of hidden attractors. Eur. Phys. J. Spec. Top. 224, 1469-1476 (2015) · doi:10.1140/epjst/e2015-02472-1
[9] Wei, Z., Wang, R., Liu, A.: A new finding of the existence of hidden hyperchaotic attractors with no equilibria. Math. Comput. Simul. 100, 13-23 (2014) · Zbl 07312592 · doi:10.1016/j.matcom.2014.01.001
[10] Sprott, J.C., Wang, X., Chen, G.: Coexistence of point, periodic and strange attractors. Int. J. Bifurc. Chaos. 23, 1350093 (2013) · doi:10.1142/S0218127413500934
[11] Sprott, J.C.: A dynamical system with a strange attractor and invariant tori. Phys. Lett. A 378, 1361-1363 (2014) · Zbl 1323.37022 · doi:10.1016/j.physleta.2014.03.028
[12] Barrio, R., Blesa, F., Serrano, S.: Qualitative analysis of the Rössler equations: bifurcations of limit cycles and chaotic attractors. Physica D 238, 1087-1100 (2009) · Zbl 1173.37049 · doi:10.1016/j.physd.2009.03.010
[13] Li, C., Sprott, J.C., Xing, H.: Hypogenetic chaotic jerk flows. Phys. Lett. A 380, 1172-1177 (2016) · doi:10.1016/j.physleta.2016.01.045
[14] Li, C., Sprott, J.C., Xing, H.: Constructing chaotic systems with conditional symmetry. Nonlinear Dyn. 87, 1351-1358 (2017) · Zbl 1372.37069 · doi:10.1007/s11071-016-3118-1
[15] Li, C., Thio, W., H. C. Iu, H., Lu T.: A memristive chaotic oscillator with increasing amplitude and frequency. IEEE Access (2018). https://doi.org/10.1109/ACCESS.2017.2788408
[16] Li, C., Sprott, J.C., Kapitaniak, T., Lu, T.: Infinite lattice of hyperchaotic strange attractors. Chaos Soliton Fractals 109, 76-82 (2018) · Zbl 1390.34115 · doi:10.1016/j.chaos.2018.02.022
[17] Thomas, R.: Deterministic chaos seen in terms of feedback circuits: analysis, synthesis, “Labyrinth Chaos”. Int. J. Bifurc. Chaos. 9, 1889-1905 (1999) · Zbl 1089.37512 · doi:10.1142/S0218127499001383
[18] Li, C., Sprott, J.C.: An infinite 3-D quasiperiodic lattice of chaotic attractors. Phys. Lett. A 382, 581-587 (2018) · Zbl 1383.35031 · doi:10.1016/j.physleta.2017.12.022
[19] Lai, Q., Akgul, A., Li, C., Xu, G., Çavuşoğlu, Ü.: A new chaotic system with multiple attractors: dynamic analysis. Circuit Realiz. S-Box Des. Entropy 20, 12 (2018). https://doi.org/10.3390/e20010012 · doi:10.3390/e20010012
[20] Akgul, A., Li, C., Pehlivan, I.: Amplitude control analysis of a four-wing chaotic attractor, its electronic circuit designs and microcontroller-based random number generator. J Circuit Syst. Comput. 26, 1750190 (2017) · doi:10.1142/S0218126617501900
[21] Yu, S., Lü, J., Chen, G., Yu, X.: Design and Implementation of grid multiwing hyperchaotic Lorenz system family via switching control and constructing super-heteroclinic loops. IEEE Trans. CAS-I: Fundam. Theor. Appl. 59, 1015-1028 (2012) · Zbl 1468.93092
[22] Wang, C., Liu, X., Hu, X.: Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system. Chaos 27, 033114 (2017) · Zbl 1390.94948 · doi:10.1063/1.4979039
[23] Wang, C., Hu, X., Zhou, L.: A memristive hyperchaotic multiscroll Jerk system with controllable scroll numbers. Int. J. Bifurc. Chaos. 27, 1750091 (2017) · Zbl 1370.34071 · doi:10.1142/S0218127417500912
[24] Lai, Q., Chen, S.: Coexisting attractors generated from a new 4D smooth chaotic system. Int. J. Control. Autom. Syst. 14, 1124-1131 (2016) · doi:10.1007/s12555-015-0056-5
[25] Li, C., Akgul, A., Sprott, J.C., H. C. Iu, H., Thio, W.: A symmetric pair of hyperchaotic attractors. Int. J. Circuit Theory Appl. 1-10 (2018). https://doi.org/10.1002/cta.2569
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.