Dynamics of the Modified n-Degree Lorenz System

[1]Lorenz, E.N., 1963. Deterministic nonperiodic flow. Journal of the atmospheric sciences, 20(2), pp.130-141.LorenzE.N.1963Deterministic nonperiodic flowJournal of the atmospheric sciences202130141Search in Google Scholar

[2]Chen, G. and Ueta, T., 1999. Yet another chaotic attractor. International Journal of Bifurcation and chaos, 9(07), pp.1465-1466.ChenG.UetaT.1999Yet another chaotic attractorInternational Journal of Bifurcation and chaos90714651466Search in Google Scholar

[3]Cuomo, K.M. and Oppenheim, A.V., 1993. Circuit implementation of synchronized chaos with applications to communications. Physical review letters, 71(1), p.65.CuomoK.M.OppenheimA.V.1993Circuit implementation of synchronized chaos with applications to communicationsPhysical review letters71165Search in Google Scholar

[4]Lü, J. and Chen, G., 2002. A new chaotic attractor coined. International Journal of Bifurcation and chaos, 12(03), pp.659-661.LüJ.ChenG.2002A new chaotic attractor coinedInternational Journal of Bifurcation and chaos1203659661Search in Google Scholar

[5]Pehlivan, I. and Uyaroğlu, Y., 2010. A new chaotic attractor from general Lorenz system family and its electronic experimental implementation. Turkish Journal of Electrical Engineering & Computer Sciences, 18(2), pp.171-184.PehlivanI.UyaroğluY.2010A new chaotic attractor from general Lorenz system family and its electronic experimental implementationTurkish Journal of Electrical Engineering & Computer Sciences182171184Search in Google Scholar

[6]Zhou, W., Xu, Y., Lu, H. and Pan, L., 2008. On dynamics analysis of a new chaotic attractor. Physics Letters A, 372(36), pp.5773-5777.ZhouW.XuY.LuH.PanL.2008On dynamics analysis of a new chaotic attractorPhysics Letters A3723657735777Search in Google Scholar

[7]Qi, G., Chen, G., Du, S., Chen, Z. and Yuan, Z., 2005. Analysis of a new chaotic system. Physica A: Statistical Mechanics and its Applications, 352(2-4), pp.295-308.QiG.ChenG.DuS.ChenZ.YuanZ.2005Analysis of a new chaotic systemPhysica A: Statistical Mechanics and its Applications3522-4295308Search in Google Scholar

[8]Tigan, G. and Opriş, D., 2008. Analysis of a 3D chaotic system. Chaos, Solitons & Fractals, 36(5), pp.1315-1319.TiganG.OprişD.2008Analysis of a 3D chaotic systemChaos, Solitons & Fractals36513151319Search in Google Scholar

[9]Robinson, R.C., 2012. An introduction to dynamical systems: continuous and discrete (Vol. 19). American Mathematical Soc..RobinsonR.C.2012An introduction to dynamical systems: continuous and discrete19American Mathematical SocSearch in Google Scholar

[10]Curry, J.H., 1978. A generalized Lorenz system. Communications in Mathematical Physics, 60(3), pp.193-204.CurryJ.H.1978A generalized Lorenz systemCommunications in Mathematical Physics603193204Search in Google Scholar

[11]Moore, D.R., Toomre, J., Knobloch, E. and Weiss, N.O., 1983. Period doubling and chaos in partial differential equations for thermosolutal convection. Nature, 303(5919), p.663.MooreD.R.ToomreJ.KnoblochE.WeissN.O.1983Period doubling and chaos in partial differential equations for thermosolutal convectionNature3035919663Search in Google Scholar

[12]Čikovský, S. and Chen, G., 2002. On a generalized Lorenz canonical form of chaotic systems. International Journal of Bifurcation and Chaos, 12(08), pp.1789-1812.ČikovskýS.ChenG.2002On a generalized Lorenz canonical form of chaotic systemsInternational Journal of Bifurcation and Chaos120817891812Search in Google Scholar

[13]Park, J.H., 2006. Chaos synchronization between two different chaotic dynamical systems. Chaos, Solitons & Fractals, 27(2), pp.549-554.ParkJ.H.2006Chaos synchronization between two different chaotic dynamical systemsChaos, Solitons & Fractals272549554Search in Google Scholar

[14]Lü, J., Chen, G., Cheng, D. and Celikovsky, S., 2002. Bridge the gap between the Lorenz system and the Chen system. International Journal of Bifurcation and Chaos, 12(12), pp.2917-2926.LüJ.ChenG.ChengD.CelikovskyS.2002Bridge the gap between the Lorenz system and the Chen systemInternational Journal of Bifurcation and Chaos121229172926Search in Google Scholar

[15]Lü, J., Chen, G. and Cheng, D., 2004. A new chaotic system and beyond: the generalized Lorenz-like system. International Journal of Bifurcation and Chaos, 14(05), pp.1507-1537.LüJ.ChenG.ChengD.2004A new chaotic system and beyond: the generalized Lorenz-like systemInternational Journal of Bifurcation and Chaos140515071537Search in Google Scholar

[16]Yu, Y., Li, H.X., Wang, S. and Yu, J., 2009. Dynamic analysis of a fractional-order Lorenz chaotic system. Chaos, Solitons & Fractals, 42(2), pp.1181-1189.YuY.LiH.X.WangSYuJ.2009Dynamic analysis of a fractional-order Lorenz chaotic systemChaos, Solitons & Fractals42211811189Search in Google Scholar

[17]Sparrow, C., 2012. The Lorenz equations: bifurcations, chaos, and strange attractors (Vol. 41). Springer Science & Business Media.SparrowC.2012The Lorenz equations: bifurcationschaos, and strange attractors (Vol. 41). Springer Science & Business MediaSearch in Google Scholar

[18]Hilborn, R.C., 2000. Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford University Press on Demand.HilbornR.C.2000Chaos and nonlinear dynamics: an introduction for scientists and engineersOxford University PressDemandSearch in Google Scholar

[19]Balibrea, F. (2016). On problems of Topological Dynamics in non-autonomous discrete systems, Applied Mathematics and Nonlinear Sciences, 1(2), 391-404.BalibreaF.2016On problems of Topological Dynamics in non-autonomous discrete systemsApplied Mathematics and Nonlinear Sciences12391404Search in Google Scholar

[20]Shvets, A., & Makaseyev, A. (2019). Deterministic chaos in pendulum systems with delay, Applied Mathematics and Nonlinear Sciences, 4(1), 1-8.ShvetsA.MakaseyevA.2019Deterministic chaos in pendulum systems with delayApplied Mathematics and Nonlinear Sciences4118Search in Google Scholar

[21]Zhu, C., 2009. Feedback control methods for stabilizing unstable equilibrium points in a new chaotic system. Nonlinear Analysis: Theory, Methods & Applications, 71(7-8), pp.2441-2446.ZhuC.2009Feedback control methods for stabilizing unstable equilibrium points in a new chaotic systemNonlinear Analysis: Theory, Methods & Applications717-824412446Search in Google Scholar

[22]Wei, Q., Yan, Z. and Ying-Hai, W., 2007. Controlling a time-delay system using multiple delay feedback control. Chinese Physics, 16(8), p.2259.WeiQ.YanZ.Ying-HaiW.2007Controlling a time-delay system using multiple delay feedback controlChinese Physics1682259Search in Google Scholar

[23]R. L. Devaney, 1990, Chaos, Fractals and Dynamics, Computer Experiments in Mathematics, Addison-Wesley, New York, NY, USA.DevaneyR. L.1990Chaos, Fractals and Dynamics, Computer Experiments in MathematicsAddison-WesleyNew York, NYUSASearch in Google Scholar

[24]U. A. M. Roslan, Some Contributions on Analysis of Chaotic Dynamical Systems, LAP Lambert Academic Publishing, Berlin, Germany, 2012RoslanU. A. M.Some Contributions on Analysis of Chaotic Dynamical SystemsLAP Lambert Academic PublishingBerlin, Germany2012Search in Google Scholar

[25]Bugce Eminaga, Hatice A. and Mustafa R., 2015, A Modified Quadratic Lorenz attractor, Arxiv 1508.06840v1 [Math.DS].BugceEminagaHaticeA.MustafaR.2015A Modified Quadratic Lorenz attractorArxiv 1508.06840v1Math.DSSearch in Google Scholar

[26]Tigan, G. and Opriş, D., 2008. Analysis of a 3D chaotic system. Chaos, Solitons & Fractals, 36(5), pp.1315-1319.TiganG.OprişD.2008Analysis of a 3D chaotic systemChaos, Solitons & Fractals36513151319Search in Google Scholar

[27]Hassan, S.S., Ahluwalia, D., Maddali, R.K. and Manglik, M., 2018. Computational dynamics of the Nicholson-Bailey models. The European Physical Journal Plus, 133(9), p.349.HassanS.S.AhluwaliaD.MaddaliR.K.ManglikM.2018Computational dynamics of the Nicholson-Bailey modelsThe European Physical Journal Plus1339349Search in Google Scholar

[28]Vaidyanathan, S., Akgul, A., Kaçar, S. and Çavuşogğlu, U., 2018. A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganography. The European Physical Journal Plus, 133(2), p.46.VaidyanathanS.AkgulA.KaçarS.ÇavuşogğluU.2018A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganographyThe European Physical Journal Plus133246Search in Google Scholar

[29]He, S., Sun, K., Mei, X., Yan, B. and Xu, S., 2017. Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative. The European Physical Journal Plus, 132(1), p.36.HeS.SunK.MeiX.YanB.XuS.2017Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivativeThe European Physical Journal Plus132136Search in Google Scholar

[30]He, S., Sun, K. and Banerjee, S., 2016. Dynamical properties and complexity in fractional-order diffusionless Lorenz system. The European Physical Journal Plus, 131(8), p.254.HeS.SunK.BanerjeeS.2016Dynamical properties and complexity in fractional-order diffusionless Lorenz systemThe European Physical Journal Plus1318254Search in Google Scholar

[31]Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285-317.WolfA.SwiftJ. B.SwinneyH. L.VastanoJ. A.1985Determining Lyapunov exponents from a time seriesPhysica D: Nonlinear Phenomena163285317Search in Google Scholar