Abstract
This paper aims at investigating the dynamics of fractional-order model of love in the fact that fractional-order derivatives could possess memories by which romantic relationships are naturally impacted. Based on the discussions of properties including the stability of equilibrium points, chaotic behaviors and typical bifurcations, we found rich dynamics exhibited by the fractional-order love system with proper fractional order and model parameters. Besides, the control problems were studied theoretically and the simulation results illustrated the effectiveness of the proposed methods.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arena, P., Caponetto, R., Fortuna, L., Porto, D.: Bifurcation and chaos in noninteger order cellular neural networks. Int. J. Bifurcat. Chaos 7, 1527–1539 (1998)
Bagley, R., Calico, R.A.: Fractional order state equations for the control of viscoelastically damped structures. J. Guid. Control dynam. 14, 304–311 (1991)
Chen, A.M., Lu, J.A., Lü, J.H., Yu, S.M.: Generating hyperchaotic Lü attractor via state feedback control. Physica A 364, 103–110 (2006)
Hartley, T.T., Lorenzo, C.F., Qammer, H.: Chaos in a fractional order Chua’s system. IEEE Trans. CAS-I 42, 485–490 (1995)
Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, New Jersey (2000)
Koeller, R.C.: Application of fractional calculus to the theory of viscoelasticity. J. Appl. Mech. 51, 294–298 (1984)
Koeller, R.C.: Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics. Acta Mech. 58, 251–264 (1986)
Li, C.P., Chen, G.: Chaos in the fractional order Chen system and its control. Chaos Soliton Fract 22, 549–554 (2004)
Li, C.P., Peng, G.J.: Chaos in Chen’s system with a fractional order. Chaos Soliton Fract 22, 443–450 (2004)
Matouk, A.E.: Dynamical analysis feedback control and synchronization of Liu dynamical system. Nonlinear Anal. 69, 3213–3224 (2008)
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)
Song, L., Xu, S.Y., Yang, M.J.: Dynamical models of happiness with fractional order. Commun. Nonlinear Sci. Numer. Simulat. 15, 616–628 (2010)
Sprott, J.C.: Dynamical models of love. Nonlinear Dyn. Psychol. Life Sci. 3, 303–314 (2004)
Sprott, J.C.: Dynamical models of happiness. Nonlinear Dyn. Psychol. Life Sci. 9, 23–36 (2005)
Strogatz, S.: Love affairs and differential equations. Math. Mag. 61, 35 (1988)
Yu, Y., Li, H., Wang, S., Yu, J.: Dynamic analysis of a fractional-order Lorenz chaotic system. Chaos Soliton Fract 42, 1181–1189 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gu, R., Xu, Y. (2011). Chaos in a Fractional-Order Dynamical Model of Love and Its Control. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_42
Download citation
DOI: https://doi.org/10.1007/978-3-642-22833-9_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22832-2
Online ISBN: 978-3-642-22833-9
eBook Packages: EngineeringEngineering (R0)