Machowski, J, Bialek, JW, Bumby, JR: Power System Dynamics: Stability and Control. Wiley, New Jersey (2008)

Google Scholar

Solovyeva, E: Mathematical Models and Stability Analysis of Induction Motors Under Sudden Changes of Load. Jyväskylä Studies in Computing, vol. 182. University of Jyväskylä, Jyväskylä (2013)

Google Scholar

Chang, YH, Wu, CI, Lin, HW, Chen, HC, Chang, CW: Fractional order integral sliding mode flux observer for direct field oriented induction machines. Int. J. Innov. Comput. Inf. Control **8**(7A), 4851-4868 (2012)

Google Scholar

Tavazoei, MS, Haeri, M: A note on the stability of fractional order systems. Math. Comput. Simul. **70**(5), 1566-1579 (2009)

Article
MathSciNet
MATH
Google Scholar

Cao, YG, Li, Y, Ren, W, Chen, YQ: Distributed coordination of networked fractional order systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. **40**(2), 362-370 (2010)

Article
Google Scholar

Podlubny, I: Fractional order systems and \(\mathrm{PI}^{\lambda}\mathrm{D}^{\mu}\) controllers. IEEE Trans. Autom. Control **44**(1), 208-213 (1999)

Article
MathSciNet
Google Scholar

Azar, AT, Vaidyanathan, S: Chaos Modeling and Control Systems Design. Springer, Berlin (2015)

Book
MATH
Google Scholar

Azar, AT, Vaidyanathan, S: Advances in Chaos Theory and Intelligent Control. Springer, Berlin (2016)

Book
MATH
Google Scholar

Vaidyanathan, S, Volos, C: Advances and Applications in Nonlinear Control Systems. Springer, Berlin (2016)

Book
MATH
Google Scholar

Vaidyanathan, S, Volos, C: Advances and Applications in Chaotic Systems. Springer, Berlin (2016)

Book
MATH
Google Scholar

Nategh, M, Baleanu, D, Valinejad, MR: On a discrete chaos induction via an aperiodic kicks pattern. J. Comput. Nonlinear Dyn. **12**(4), 041008 (2017)

Article
Google Scholar

Yang, J, Zhao, L: Bifurcation analysis and chaos control of the modified Chua’s circuit system. Chaos Solitons Fractals **77**, 332-339 (2015)

Article
MathSciNet
MATH
Google Scholar

Sundarapandian, V, Karthikeyan, R: Hybrid synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems via active control. J. Eng. Appl. Sci. **7**(3), 254-264 (2012)

Google Scholar

Karthikeyan, R, Sundarapandian, V: Hybrid chaos synchronization of four-scroll systems via active control. J. Electr. Eng. **65**(2), 97-103 (2014)

Google Scholar

Vaidyanathan, S, Azar, AT, Rajagopal, K, Alexander, P: Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control. Int. J. Model. Identif. Control **23**(3), 267-277 (2015)

Article
Google Scholar

Vaidyanathan, S: Active control design for the anti-synchronization of Lotka-Volterra biological systems with four competitive species. Int. J. PharmTech Res. **8**(7), 58-70 (2015)

MathSciNet
Google Scholar

Pehlivan, I, Moroz, IM, Vaidyanathan, S: Analysis, synchronization and circuit design of a novel butterfly attractor. J. Sound Vib. **333**(20), 5077-5096 (2014)

Article
Google Scholar

Vaidyanathan, S, Rajagopal, K: Analysis, control, synchronization and LabVIEW implementation of a seven-term novel chaotic system. Int. J. Control Theory Appl. **9**(1), 151-174 (2016)

Google Scholar

Vaidyanathan, S: Synchronization of Tokamak systems with symmetric and magnetically confined plasma via adaptive control. Int. J. ChemTech Res. **8**(6), 818-827 (2015)

Google Scholar

Vaidyanathan, S: Anti-synchronization of Rikitake two-disk dynamo chaotic systems via adaptive control method. Int. J. ChemTech Res. **8**(9), 393-405 (2015)

MathSciNet
Google Scholar

Vaidyanathan, S, Rajagopal, K: Adaptive control, synchronization and LabVIEW implementation of Rucklidge chaotic system for nonlinear double convection. Int. J. Control Theory Appl. **9**(1), 175-197 (2016)

Google Scholar

Yau, HT: Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos Solitons Fractals **22**(2), 341-347 (2004)

Article
MathSciNet
MATH
Google Scholar

Vaidyanathan, S, Boulkroune, A: A novel hyperchaotic system with two quadratic nonlinearities, its analysis and synchronization via integral sliding mode control. Int. J. Control Theory Appl. **9**(1), 321-337 (2016)

Google Scholar

Vaidyanathan, S, Sampath, S, Azar, AT: Global chaos synchronization of identical chaotic systems via novel sliding mode control method and its application to Zhu system. Int. J. Model. Identif. Control **23**(1), 92-100 (2015)

Article
Google Scholar

Sampath, S, Vaidyanathan, S: Hybrid synchronization of identical chaotic systems via novel sliding control method with application to Sampath four-scroll chaotic system. Int. J. Control Theory Appl. **9**(1), 221-235 (2016)

Google Scholar

Wang, C, Ge, SS: Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos Solitons Fractals **12**(7), 1199-1206 (2001)

Article
MATH
Google Scholar

Vaidyanathan, S: A novel hyperchaotic hyperjerk system with two nonlinearities, its analysis, adaptive control and synchronization via backstepping control method. Int. J. Control Theory Appl. **9**(1), 257-278 (2016)

Google Scholar

Vaidyanathan, S, Rasappan, S: Global chaos synchronization of *n*-scroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arab. J. Sci. Eng. **39**(4), 3351-3364 (2014)

Article
Google Scholar

Senouci, A, Boukabou, A: Fuzzy modeling, stabilization and synchronization of multi-scroll chaotic systems. Optik **127**(13), 5351-5358 (2016)

Article
Google Scholar

Vaidyanathan, S, Azar, AT: Takagi-Sugeno fuzzy logic controller for Liu-Chen four-scroll chaotic system. Int. J. Intell. Eng. Inform. **4**(2), 135-150 (2016)

Google Scholar

Revel, G, Leon, AE, Alonso, DM, Moiola, JL: Multi-parameter bifurcation analysis of subsynchronous interactions in DFIG-based wind farms. Electr. Power Syst. Res. **140**, 643-652 (2016)

Article
Google Scholar

Zarei, A, Tavakoli, S: Hopf bifurcation analysis and ultimate bound estimation of a new 4-D quadratic autonomous hyper-chaotic system. Appl. Math. Comput. **291**, 323-339 (2016)

MathSciNet
Google Scholar

Kuznetsov, YA: Elements of Applied Bifurcation Theory. Springer, Berlin (1995)

Book
MATH
Google Scholar

Jabli, N, Khammari, H, Mimouni, MF, Dhifaoui, R: Bifurcation and chaos phenomena appearing in induction motor under variation of PI controller parameters. WSEAS Trans. Syst. **9**(7), 784-793 (2010)

MATH
Google Scholar

Sundarapandian, V, Pehlivan, I: Analysis, control, synchronization and circuit design of a novel chaotic system. Math. Comput. Model. **55**(7-8), 1904-1915 (2012)

Article
MathSciNet
MATH
Google Scholar

Li, Y, Chen, Y, Podlubny, I: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. **59**(5), 1810-1821 (2010)

Article
MathSciNet
MATH
Google Scholar

Gallegos, JA, Duarte-Mermoud, MA: On the Lyapunov theory for fractional order systems. Appl. Math. Comput. **287**, 161-170 (2016)

MathSciNet
MATH
Google Scholar

Tavazoei, MS, Haeri, M: Chaos control via a simple fractional order controller. Phys. Lett. A **372**, 798-807 (2008)

Article
MATH
Google Scholar

Konishi, K, Kokame, H, Hara, N: Delayed feedback control based on the act-and-wait concept. Nonlinear Dyn. **63**, 513-519 (2011)

Article
Google Scholar

Jin, Y, Chen, YQ, Xue, D: Time-constant robust analysis of a fractional order [proportional derivative] controller. IET Control Theory Appl. **5**(1), 164-172 (2011)

Article
Google Scholar

Vaidyanathan, S, Rajagopal, K, Volos, C, Kyprianidis, IM, Stouboulos, IN: Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in LabVIEW. J. Eng. Sci. Technol. Rev. **8**(2), 130-141 (2015)

Google Scholar

Chen, D, Shi, P, Ma, X: Control and synchronization of chaos in an induction motor system. Int. J. Innov. Comput. Inf. Control **8**(10B), 7237-7248 (2012)

Google Scholar

Li, H, Liao, X, Luo, M: A novel non-equilibrium fractional order chaotic system and its complete synchronization by circuit implementation. Nonlinear Dyn. **68**(1), 137-149 (2012)

Article
MathSciNet
MATH
Google Scholar

Petras, I: A note on the fractional order Chua’s system. Chaos Solitons Fractals **38**(1), 140-147 (2008)

Article
Google Scholar

Katugampola, UN: A new approach to generalized fractional derivatives. Bull. Math. Anal. Appl. **6**(4), 1-15 (2014)

MathSciNet
MATH
Google Scholar

Herzallah, MAE: Notes on some fractional calculus operators and their properties. J. Fract. Calc. Appl. **5**(19), 1-10 (2014)

MathSciNet
Google Scholar

Rajagopal, K, Vaidyanathan, S, Karthikeyan, A, Duraisamy, P: Dynamic analysis and chaos suppression in a fractional order brushless DC motor. Electr. Eng. (2016). doi:10.1007/s00202-016-0444-8

Google Scholar

Jafari, S, Sprott, JC: Simple chaotic flows with a line equilibrium. Chaos Solitons Fractals **57**, 79-84 (2013)

Article
MathSciNet
MATH
Google Scholar

Jafari, S, Sprott, JC, Golpayegani, SMRH: Elementary quadratic chaotic flows with no equilibria. Phys. Lett. A **377**(9), 699-702 (2013)

Article
MathSciNet
Google Scholar

Pham, VT, Volos, C, Jafari, S, Wang, X, Vaidyanathan, S: Hidden hyperchaotic attractor in a novel simple memristive neural network. Optoelectron. Adv. Mater., Rapid Commun. **8**(11-12), 1157-1163 (2014)

Google Scholar

Pham, VT, Volos, C, Jafari, S, Wei, Z, Wang, X: Constructing a novel no-equilibrium chaotic system. Int. J. Bifurc. Chaos Appl. Sci. Eng. **24**(5), Article ID 1450073 (2014)

Article
MathSciNet
MATH
Google Scholar

Jafari, S, Sprott, JC, Nazarimehr, F: Recent new examples of hidden attractors. Eur. Phys. J. Spec. Top. **224**(8), 1469-1476 (2015)

Article
Google Scholar

Sprott, JC, Jafari, S, Pham, VT, Hosseini, ZS: A chaotic system with a single unstable node. Phys. Lett. A **379**(36), 2030-2036 (2015)

Article
MathSciNet
MATH
Google Scholar

Rajagopal, K, Laarem, G, Karthikeyan, A, Srinivasan, A, Adam, G: Fractional order memristor no equilibrium chaotic system with its adaptive sliding mode synchronization and genetically optimized fractional order PID synchronization. Complexity **2017**, Article ID 1892618 (2017)

MathSciNet
MATH
Google Scholar

Rajagopal, K, Karthikeyan, A, Srinivasan, A: FPGA implementation of novel fractional order chaotic system with two equilibriums and no equilibrium and its adaptive sliding mode synchronization. Nonlinear Dyn. **87**(4), 2281-2304 (2017)

Article
Google Scholar

Baleanua, D, Wu, G, Zeng, S: Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations. Chaos Solitons Fractals (2017). doi:10.1016/j.chaos.2017.02.007

MathSciNet
Google Scholar

Jajarmi, A, Hajipour, M, Baleanu, D: New aspects of the adaptive synchronization and hyperchaos suppression of a financial model. Chaos Solitons Fractals **99**, 285-296 (2017)

Article
MathSciNet
Google Scholar

Astrom, KJ, Hagglund, T: PID Controllers: Theory, Design and Tuning. Research Triangle Park, North Carolina (1995)

Google Scholar

Goldberg, DE: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)

MATH
Google Scholar

Wang, Q, Spronck, P, Tracht, R: An overview of genetic algorithms applied to control engineering problems. In: Proceedings of the Second International Conference on Machine Learning and Cybernetics, Xi’an, 3-5 Nov. 2003 (2003). doi:10.1109/ICMLC.2003.1259761

Google Scholar

Chen, Z, Yuan, X, Ji, B, Wang, P, Tian, H: Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II. Energy Convers. Manag. **84**, 390-404 (2014)

Article
Google Scholar

Pezeshki, C: Bispectral analysis of systems possessing chaotic motions. J. Sound Vib. **137**(3), 357-368 (1990)

Article
MathSciNet
MATH
Google Scholar

Chandran, V, Elgar, S, Pezeshki, C: Bispectral and trispectral characterization of transition to chaos in the Duffing oscillator. Int. J. Bifurc. Chaos Appl. Sci. Eng. **3**(3), 551-557 (1993)

Article
MathSciNet
MATH
Google Scholar