Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

References

• Aghababa, M. P., & Feizi, H. (2012). Design of a sliding mode controller for synchronizing chaotic systems with parameter and model uncertainties and external disturbances. Transactions of the Institute of Measurement and Control, 34(8), 990–997.
   Web of Science ®Google Scholar
• Bayat, F., Mobayen, S., & Javadi, S. (2016). Finite-time tracking control of nth-order chained-form non-holonomic systems in the presence of disturbances. ISA Transactions, 63, 78–83.
   PubMed Web of Science ®Google Scholar
• Bier, M., & Bountis, T. C. (1984). Remerging Feigenbaum trees in dynamical systems. Physics Letters A, 104(5), 239–244.
   Web of Science ®Google Scholar
• Bragin, V., Vagaitsev, V., Kuznetsov, N., & Leonov, G. (2011). Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits. Journal of Computer and Systems Sciences International, 50(4), 511–543.
   Web of Science ®Google Scholar
• Brummitt, C. D., & Sprott, J. (2009). A search for the simplest chaotic partial differential equation. Physics Letters A, 373(31), 2717–2721.
   Web of Science ®Google Scholar
• Chen, G., & Ueta, T. (1999). Yet another chaotic attractor. International Journal of Bifurcation and Chaos, 9(7), 1465–1466.
   Web of Science ®Google Scholar
• Cheng, Y., Du, H., He, Y., & Jia, R. (2015). Robust finite-time synchronization of coupled harmonic oscillations with external disturbance. Journal of the Franklin Institute, 352(10), 4366–4381.
   Web of Science ®Google Scholar
• Dawson, S. P., Grebogi, C., Yorke, J. A., Kan, I., & Koçak, H. (1992). Antimonotonicity: Inevitable reversals of period-doubling cascades. Physics Letters A, 162(3), 249–254.
   Web of Science ®Google Scholar
• Dudkowski, D., Jafari, S., Kapitaniak, T., Kuznetsov, N. V., Leonov, G. A., & Prasad, A. (2016). Hidden attractors in dynamical systems. Physics Reports, 637, 1–50. doi:10.1016/j.physrep.2016.05.002
   Web of Science ®Google Scholar
• Golestani, M., Mobayen, S., & Tchier, F. (2016). Adaptive finite-time tracking control of uncertain non-linear n-order systems with unmatched uncertainties. IET Control Theory & Applications, 10(14), 1675–1683.
   Web of Science ®Google Scholar
• Gotthans, T., & Petržela, J. (2015). New class of chaotic systems with circular equilibrium. Nonlinear Dynamics, 81(3), 1143–1149.
   Web of Science ®Google Scholar
• Gottlieb, H., & Sprott, J. (2001). Simplest driven conservative chaotic oscillator. Physics Letters A, 291(6), 385–388.
   Web of Science ®Google Scholar
• Jafari, S., Pham, V.-T., & Kapitaniak, T. (2016). Multiscroll chaotic sea obtained from a simple 3d system without equilibrium. International Journal of Bifurcation and Chaos, 26(2), 1650031
   Web of Science ®Google Scholar
• Jafari, S., & Sprott, J. (2013). Simple chaotic flows with a line equilibrium. Chaos, Solitons & Fractals, 57, 79–84.
   Web of Science ®Google Scholar
• Jafari, S., Sprott, J., & Molaie, M. (2016). A simple chaotic flow with a plane of equilibria. International Journal of Bifurcation and Chaos, 26(6), 1650098
   Web of Science ®Google Scholar
• Jafari, S., & Sprott, J. C. (2013). Simple chaotic flows with a line equilibrium. Chaos, Solitons & Fractals, 57, 79–84.
   Web of Science ®Google Scholar
• Jafari, S., Sprott, J. C., & Hashemi Golpayegani, S. M. R. (2013). Elementary quadratic chaotic flows with no equilibria. Physics Letters A, 377(9), 699–702.
   Web of Science ®Google Scholar
• Jafari, S., Sprott, J. C., & Molaie, M. (2016). A simple chaotic flow with a plane of equilibria. International Journal of Bifurcation and Chaos, 26(6), 1650098.
   Web of Science ®Google Scholar
• Jafari, S., Sprott, J. C., & Nazarimehr, F. (2015). Recent new examples of hidden attractors. The European Physical Journal Special Topics, 224(8), 1469–1476.
   Web of Science ®Google Scholar
• Jafari, S., Sprott, J. C., Pham, V.-T., Hashemi Golpayegani, S. M. R., & Jafari, A. H. (2014). A new cost function for parameter estimation of chaotic systems using return maps as fingerprints. International Journal of Bifurcation and Chaos, 24(10), 1450134.
   Web of Science ®Google Scholar
• Jafari, S., Sprott, J. C., Pham, V.-T., Volos, C., & Li, C. (2016). Simple chaotic 3D flows with surfaces of equilibria. Nonlinear Dynamics, 86(2), 1349–1358. doi:10.1007/s11071-016-2968-x
   Web of Science ®Google Scholar
• Jun-Kang, N., Chong-Xin, L., Kai, L., & Ling, L. (2014). Finite-time sliding mode synchronization of chaotic systems. Chinese Physics B, 23(10), 100504.
   Web of Science ®Google Scholar
• Khanzadeh, A., & Pourgholi, M. (2016). Robust synchronization of fractional-order chaotic systems at a pre-specified time using sliding mode controller with time-varying switching surfaces. Chaos, Solitons & Fractals, 91, 69–77.
   Web of Science ®Google Scholar
• Kingni, S. T., Jafari, S., Simo, H., & Woafo, P. (2014). Three-dimensional chaotic autonomous system with only one stable equilibrium: Analysis, circuit design, parameter estimation, control, synchronization and its fractional-order form. The European Physical Journal Plus, 129(5), 1–16.
   Web of Science ®Google Scholar
• Kingni, S., Nana, B., Ngueuteu, G. M., Woafo, P., & Danckaert, J. (2015). Bursting oscillations in a 3D system with asymmetrically distributed equilibria: Mechanism, electronic implementation and fractional derivation effect. Chaos, Solitons & Fractals, 71, 29–40.
   Web of Science ®Google Scholar
• Kingni, S. T., Pham, V.-T., Jafari, S., Kol, G. R., & Woafo, P. (2016). Three-dimensional chaotic autonomous system with a circular equilibrium: Analysis, circuit implementation and its fractional-order form. Circuits, Systems, and Signal Processing, 35(6), 1933–1948.
   Web of Science ®Google Scholar
• Kiseleva, M., Kudryashova, E., Kuznetsov, N., Kuznetsova, O., Leonov, G., Yuldashev, M., & Yuldashev, R. (2017). Hidden and self-excited attractors in Chua circuit: Synchronization and SPICE simulation. International Journal of Parallel, Emergent and Distributed Systems, 1–11.
   Google Scholar
• Kuznetsov, N., Leonov, G., Yuldashev, M., & Yuldashev, R. (2017). Hidden attractors in dynamical models of phase-locked loop circuits: Limitations of simulation in MATLAB and SPICE. Communications in Nonlinear Science and Numerical Simulation, 51, 39–49.
   Web of Science ®Google Scholar
• Kyprianidis, I., Stouboulos, I., Haralabidis, P., & Bountis, T. (2000). Antimonotonicity and chaotic dynamics in a fourth-order autonomous nonlinear electric circuit. International Journal of Bifurcation and Chaos, 10(8), 1903–1915.
   Web of Science ®Google Scholar
• Leonov, G., & Kuznetsov, N. (2011). Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems. IFAC Proceedings Volumes (IFAC-PapersOnline), 18(1), 2494–2505.
   Google Scholar
• Leonov, G., Kuznetsov, N., Kiseleva, M., Solovyeva, E., & Zaretskiy, A. (2014). Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor. Nonlinear Dynamics, 77(1–2), 277–288.
   Web of Science ®Google Scholar
• Leonov, G., Kuznetsov, N., Kuznetsova, O., Seledzhi, S., & Vagaitsev, V. (2011). Hidden oscillations in dynamical systems. Transaction on Systems and Control, 6(2), 54–67.
   Google Scholar
• Leonov, G., Kuznetsov, N., & Mokaev, T. (2015a). Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity. Communications in Nonlinear Science and Numerical Simulation, 28(1), 166–174.
   Web of Science ®Google Scholar
• Leonov, G., Kuznetsov, N., & Mokaev, T. (2015b). Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion. The European Physical Journal Special Topics, 224(8), 1421–1458.
   Web of Science ®Google Scholar
• Leonov, G., Kuznetsov, N., & Vagaitsev, V. (2012). Hidden attractor in smooth Chua systems. Physica D: Nonlinear Phenomena, 241(18), 1482–1486.
   Web of Science ®Google Scholar
• Leonov, G. A., & Kuznetsov, N. V. (2013). Hidden attractors in dynamical systems. From hidden oscillations in Hilbert–Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits. International Journal of Bifurcation and Chaos, 23(1), 1330002.
   Web of Science ®Google Scholar
• Li, C., Hu, W., Sprott, J. C., & Wang, X. (2015). Multistability in symmetric chaotic systems. The European Physical Journal Special Topics, 224(8), 1493–1506.
   Web of Science ®Google Scholar
• Li, F., & Yao, C. (2016). The infinite-scroll attractor and energy transition in chaotic circuit. Nonlinear Dynamics , 84 (4), 2305–2315.
   Web of Science ®Google Scholar
• Li, L., & Jian, J. (2014). Finite-time synchronization of chaotic complex networks with stochastic disturbance. Entropy, 17(1), 39–51.
   Web of Science ®Google Scholar
• Liu, J. F. S. (2007). A novel dynamic terminal sliding mode control of uncertain nonlinear systems. Journal of Control Theory and Applications, 5, 189–193.
   Google Scholar
• Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130–141.
   Web of Science ®Google Scholar
• Lü, J., & Chen, G. (2006). Generating multiscroll chaotic attractors: Theories, methods and applications. International Journal of Bifurcation and Chaos, 16(4), 775–858.
   Web of Science ®Google Scholar
• Ma, J., Wu, X., Chu, R., & Zhang, L. (2014). Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice. Nonlinear Dynamics, 76(4), 1951–1962.
   Web of Science ®Google Scholar
• Majd, V. J., & Mobayen, S. (2015). An ISM-based CNF tracking controller design for uncertain MIMO linear systems with multiple time-delays and external disturbances. Nonlinear Dynamics, 80(1–2), 591–613.
   Web of Science ®Google Scholar
• Mobayen, S. (2014a). Design of CNF-based nonlinear integral sliding surface for matched uncertain linear systems with multiple state-delays. Nonlinear Dynamics, 77(3), 1047–1054.
   Web of Science ®Google Scholar
• Mobayen, S. (2014b). Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback. Nonlinear Dynamics, 76(1), 827–838.
   Web of Science ®Google Scholar
• Mobayen, S. (2015a). An adaptive chattering-free PID sliding mode control based on dynamic sliding manifolds for a class of uncertain nonlinear systems. Nonlinear Dynamics, 82(1–2), 53–60.
   Web of Science ®Google Scholar
• Mobayen, S. (2015b). An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems. Nonlinear Dynamics, 82(1–2), 599–610.
   Web of Science ®Google Scholar
• Mobayen, S. (2015c). Design of a robust tracker and disturbance attenuator for uncertain systems with time delays. Complexity, 21(1), 340–348.
   Web of Science ®Google Scholar
• Mobayen, S. (2015d). Design of LMI‐based global sliding mode controller for uncertain nonlinear systems with application to Genesio's chaotic system. Complexity, 21(1), 94–98.
   Web of Science ®Google Scholar
• Mobayen, S. (2015e). Fast terminal sliding mode controller design for nonlinear second‐order systems with time‐varying uncertainties. Complexity, 21(2), 239–244.
   Web of Science ®Google Scholar
• Mobayen, S. (2015f). Fast terminal sliding mode tracking of non-holonomic systems with exponential decay rate. IET Control Theory & Applications, 9(8), 1294–1301.
   Web of Science ®Google Scholar
• Mobayen, S. (2015g). Finite-time tracking control of chained-form nonholonomic systems with external disturbances based on recursive terminal sliding mode method. Nonlinear Dynamics, 80(1–2), 669–683.
   Web of Science ®Google Scholar
• Mobayen, S. (2015h). An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems. Nonlinear Dynamics, 79(2), 1075–1084.
   Web of Science ®Google Scholar
• Mobayen, S. (2015i). An LMI-based robust tracker for uncertain linear systems with multiple time-varying delays using optimal composite nonlinear feedback technique. Nonlinear Dynamics, 80(1–2), 917–927.
   Web of Science ®Google Scholar
• Mobayen, S. (2016a). Design of LMI‐based sliding mode controller with an exponential policy for a class of underactuated systems. Complexity, 21(5), 117–124.
   Web of Science ®Google Scholar
• Mobayen, S. (2016b). Finite-time robust-tracking and model-following controller for uncertain dynamical systems. Journal of Vibration and Control, 22(4), 1117–1127.
   Web of Science ®Google Scholar
• Mobayen, S. (2016c). Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach. Complexity, 21(5), 14–19.
   Web of Science ®Google Scholar
• Mobayen, S. (2016d). A novel global sliding mode control based on exponential reaching law for a class of underactuated systems with external disturbances. Journal of Computational and Nonlinear Dynamics, 11(2), 021011.
   Web of Science ®Google Scholar
• Mobayen, S. (2016e). Optimal LMI‐based state feedback stabilizer for uncertain nonlinear systems with time‐varying uncertainties and disturbances. Complexity, 21(6), 356–362.
   Web of Science ®Google Scholar
• Mobayen, S., & Baleanu, D. (2016). Stability analysis and controller design for the performance improvement of disturbed nonlinear systems using adaptive global sliding mode control approach. Nonlinear Dynamics, 83(3), 1557–1565.
   Web of Science ®Google Scholar
• Mobayen, S., & Baleanu, D. (2017). Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control. Journal of Vibration and Control, 23(8), 1285–1295.
   Web of Science ®Google Scholar
• Mobayen, S., Baleanu, D., & Tchier, F. (2016). Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems. Journal of Vibration and Control, 23(18), 2912–2925. doi: 1077546315623887.
   Web of Science ®Google Scholar
• Mobayen, S., & Javadi, S. (2017). Disturbance observer and finite-time tracker design of disturbed third-order nonholonomic systems using terminal sliding mode. Journal of Vibration and Control, 23(2), 181–189.
   Web of Science ®Google Scholar
• Mobayen, S., & Majd, V. J. (2012). Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances. Nonlinear Dynamics, 70(1), 171–180.
   Web of Science ®Google Scholar
• Mobayen, S., Majd, V. J., & Sojoodi, M. (2012). An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems. Mathematics and Computers in Simulation, 85, 1–10.
   Web of Science ®Google Scholar
• Mobayen, S., & Tchier, F. (2015). A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems. Kybernetika, 51(6), 1035–1048.
   Web of Science ®Google Scholar
• Mobayen, S., & Tchier, F. (2016). Design of an adaptive chattering avoidance global sliding mode tracker for uncertain non-linear time-varying systems. Transactions of the Institute of Measurement and Control., 39(10), 1547–1558. doi: 0142331216644046.
   Web of Science ®Google Scholar
• Mobayen, S., & Tchier, F. (2017a). Nonsingular fast terminal sliding mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer. Scientia Iranica, 24(3), 1410–1418.
   Web of Science ®Google Scholar
• Mobayen, S., & Tchier, F. (2017b). Composite nonlinear feedback control technique for master/slave synchronization of nonlinear systems. Nonlinear Dynamics, 87(3), 1731–1747.
   Web of Science ®Google Scholar
• Mobayen, S., & Tchier, F. (2018). Synchronization of a class of uncertain chaotic systems with Lipschitz nonlinearities using state‐feedback control design: A matrix inequality approach. Asian Journal of Control, 20(01), 1–15. doi: 10.1002/asjc.1512
   Web of Science ®Google Scholar
• Mobayen, S., Tchier, F., & Ragoub, L. (2017). Design of an adaptive tracker for n-link rigid robotic manipulators based on super-twisting global nonlinear sliding mode control. International Journal of Systems Science, 48(9), 1990–2002.
   Web of Science ®Google Scholar
• Mobayen, S., Yazdanpanah, M. J., & Majd, V. J. (2011). A finite-time tracker for nonholonomic systems using recursive singularity-free FTSM. In American Control Conference (pp. 1720–1725), San Francisco, CA, USA: IEEE.
   Google Scholar
• Molaie, M., Jafari, S., Sprott, J. C., & Hashemi Golpayegani, S. M. R. (2013). Simple chaotic flows with one stable equilibrium. International Journal of Bifurcation and Chaos, 23(11), 1350188
   Web of Science ®Google Scholar
• Muñoz-Pacheco, J., Tlelo-Cuautle, E., Toxqui-Toxqui, I., Sánchez-López, C., & Trejo-Guerra, R. (2014). Frequency limitations in generating multi-scroll chaotic attractors using CFOAs. International Journal of Electronics, 101(11), 1559–1569.
   Web of Science ®Google Scholar
• Nana, B., & Woafo, P. (2015). Chaotic masking of communication in an emitter–relay–receiver electronic setup. Nonlinear Dynamics, 82(1–2), 899–908.
   Web of Science ®Google Scholar
• Nazarimehr, F., Saedi, B., Jafari, S., & Sprott, J. (2017). Are perpetual points sufficient for locating hidden attractors?, International Journal of Bifurcation and Chaos, 28(03).
   Google Scholar
• Pham, V.-T., Volos, C., Jafari, S., Wei, Z., & Wang, X. (2014). Constructing a novel no-equilibrium chaotic system. International Journal of Bifurcation and Chaos, 24(5), 1450073
   Web of Science ®Google Scholar
• Rössler, O. E. (1976). An equation for continuous chaos. Physics Letters A, 57(5), 397–398.
   Web of Science ®Google Scholar
• Sharma, P. R., Shrimali, M. D., Prasad, A., Kuznetsov, N., & Leonov, G. (2015). Controlling dynamics of hidden attractors. International Journal of Bifurcation and Chaos, 25(4), 1550061.
   Web of Science ®Google Scholar
• Shi, L., Yang, X., Li, Y., & Feng, Z. (2016). Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations. Nonlinear Dynamics, 83(1–2), 75–87.
   Web of Science ®Google Scholar
• Shi, X., Wang, Z., & Han, L. (2017). Finite-time stochastic synchronization of time-delay neural networks with noise disturbance. Nonlinear Dynamics, 88(4), 2747–2755.
   Web of Science ®Google Scholar
• Sprott, J. C. (1994). Some simple chaotic flows. Physical Review E, 50(2), R647.
   PubMed Web of Science ®Google Scholar
• Sprott, J. C. (2000). Simple chaotic systems and circuits. American Journal of Physics, 68(8), 758–763.
   Web of Science ®Google Scholar
• Sprott, J. C. (2014). Simplest chaotic flows with involutional symmetries. International Journal of Bifurcation and Chaos, 24(1), 1450009.
   Web of Science ®Google Scholar
• Sprott, J. C. (2015). Symmetric time-reversible flows with a strange attractor. International Journal of Bifurcation and Chaos, 25(5), 1550078.
   Web of Science ®Google Scholar
• Sprott, J. C., Jafari, S., Khalaf, A. J. M., & Kapitaniak, T. (2017). Megastability: Coexistence of a countable infinity of nested attractors in a periodically-forced oscillator with spatially-periodic damping. The European Physical Journal Special Topics, 226(9), 1979–1985.
   Web of Science ®Google Scholar
• Sprott, J. C., Jafari, S., Pham, V.-T., & Hosseini, Z. S. (2015). A chaotic system with a single unstable node. Physics Letters A, 379(36), 2030–2036. doi:https://doi.org/10.1016/j.physleta.2015.06.039
   Web of Science ®Google Scholar
• Sprott, J. C., & Linz, S. J. (2000). Algebraically simple chaotic flows. International Journal of Chaos Theory and Applications, 5(2), 1–20.
   Google Scholar
• Tang, W. K., Zhong, G., Chen, G., & Man, K. (2001). Generation of n-scroll attractors via sine function. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48(11), 1369–1372.
   Google Scholar
• Tlelo-Cuautle, E., Rangel-Magdaleno, J., Pano-Azucena, A., Obeso-Rodelo, P., & Nunez-Perez, J. (2015). FPGA realization of multi-scroll chaotic oscillators. Communications in Nonlinear Science and Numerical Simulation, 27(1), 66–80.
   Web of Science ®Google Scholar
• Vaseghi, B., Pourmina, M. A., & Mobayen, S. (2017). Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding mode control. Nonlinear Dynamics, 89(03), 1689–-1704. doi:10.1007/s11071-017-3543-9
   Web of Science ®Google Scholar
• Volos, C. K., Kyprianidis, I. M., & Stouboulos, I. N. (2012). A chaotic path planning generator for autonomous mobile robots. Robotics and Autonomous Systems, 60(4), 651–656.
   Web of Science ®Google Scholar
• Wang, L. (2009). 3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system. Nonlinear dynamics, 56(4), 453–462.
   Web of Science ®Google Scholar
• Wang, Y., Guan, Z.-H., & Wen, X. (2004). Adaptive synchronization for Chen chaotic system with fully unknown parameters. Chaos, Solitons & Fractals, 19(4), 899–903.
   Web of Science ®Google Scholar
• Wei, Z. (2011). Dynamical behaviors of a chaotic system with no equilibria. Physics Letters A, 376(2), 102–108.
   Web of Science ®Google Scholar
• Wei, Z., Moroz, I., & Liu, A. (2014). Degenerate Hopf bifurcations, hidden attractors, and control in the extended Sprott E system with only one stable equilibrium. Turkish Journal of Mathematics, 38(4), 672–687.
   Web of Science ®Google Scholar
• Wei, Z., Sprott, J., & Chen, H. (2015). Elementary quadratic chaotic flows with a single non-hyperbolic equilibrium. Physics Letters A, 379(37), 2184–2187.
   Web of Science ®Google Scholar
• Wei, Z., Tang, Y., Chen, H., & Pehlivan, I. (2013). Adaptive reduced-order function projective synchronization and circuit design of hyperchaotic DLE with no equilibria. Optoelectronics and Advanced Materials-Rapid Communications, 7(11–12), 984–990.
   Web of Science ®Google Scholar
• Wei, Z., Wang, R., & Liu, A. (2014). A new finding of the existence of hidden hyperchaotic attractors with no equilibria. Mathematics and Computers in Simulation, 100, 13–23.
   Web of Science ®Google Scholar
• Wei, Z., & Zhang, W. (2014). Hidden hyperchaotic attractors in a modified Lorenz–Stenflo system with only one stable equilibrium. International Journal of Bifurcation and Chaos, 24(10), 1450127.
   Web of Science ®Google Scholar
• Wei, Z., Zhang, W., & Yao, M. (2015). On the periodic orbit bifurcating from one single non-hyperbolic equilibrium in a chaotic jerk system. Nonlinear Dynamics, 82(3), 1251–1258.
   Web of Science ®Google Scholar
• Wu, H., Zhang, X., Li, R., & Yao, R. (2015). Finite-time synchronization of chaotic neural networks with mixed time-varying delays and stochastic disturbance. Memetic Computing, 7(3), 231–240.
   Web of Science ®Google Scholar
• Xi, X., Mobayen, S., Ren, H., & Jafari, S. (2017). Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control. Journal of Vibration and Control. doi:1077546317713532.
   Web of Science ®Google Scholar
• Yalcin, M. E., Suykens, J. A., & Vandewalle, J. (2004). True random bit generation from a double-scroll attractor. IEEE transactions on circuits and Systems I: Regular Papers, 51(7), 1395–1404.
   Web of Science ®Google Scholar
• Yin, C., Chen, Y., & Zhong, S.-M. (2014). Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems. Automatica, 50(12), 3173–3181.
   Web of Science ®Google Scholar
• Yin, C., Cheng, Y., Chen, Y., Stark, B., & Zhong, S. (2015). Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems. Nonlinear Dynamics, 82(1–2), 39–52.
   Web of Science ®Google Scholar
• Yin, C., Huang, X., Chen, Y., Dadras, S., Zhong, S.-m., & Cheng, Y. (2017). Fractional-order exponential switching technique to enhance sliding mode control. Applied Mathematical Modelling, 44, 705–726.
   Web of Science ®Google Scholar
• Zuo, T., Sun, K., Ai, X., & Wang, H. (2014). High-order grid multiscroll chaotic attractors generated by the second-generation current conveyor circuit. IEEE Transactions on Circuits and Systems II: Express Briefs, 61(10), 818–822.
   Web of Science ®Google Scholar