Bifurcations and chaos in a discrete SI epidemic model with fractional order

[1]  Jinde Cao,et al.  Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons , 2018, Commun. Nonlinear Sci. Numer. Simul..

[2]  Tarynn M. Witten,et al.  Mathematical analysis of an influenza A epidemic model with discrete delay , 2017, J. Comput. Appl. Math..

[3]  Jinde Cao,et al.  New bifurcation results for fractional BAM neural network with leakage delay , 2017 .

[4]  Deccy Y. Trejos,et al.  A discrete epidemic model for bovine Babesiosis disease and tick populations , 2017 .

[5]  Jinde Cao,et al.  Controlling bifurcation in a delayed fractional predator-prey system with incommensurate orders , 2017, Appl. Math. Comput..

[6]  Chin-Chin Wu Existence of traveling waves with the critical speed for a discrete diffusive epidemic model , 2017 .

[7]  A. E. Matouk,et al.  Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization , 2014, Journal of Applied Mathematics and Computing.

[8]  Qigui Yang,et al.  Bifurcation, invariant curve and hybrid control in a discrete-time predator–prey system , 2015 .

[9]  Kamel Al-khaled,et al.  An approximate solution for a fractional model of generalized Harry Dym equation , 2014 .

[10]  S. Salman,et al.  On a discretization process of fractional-order Logistic differential equation , 2014 .

[11]  Max O. Souza,et al.  Discrete and continuous SIS epidemic models: A unifying approach , 2014 .

[12]  Zhidong Teng,et al.  Stability and bifurcation analysis in a discrete SIR epidemic model , 2014, Math. Comput. Simul..

[13]  Yicang Zhou,et al.  The stability and bifurcation analysis of a discrete Holling-Tanner model , 2013 .

[14]  R. Agarwal,et al.  Fractional-order Chua’s system: discretization, bifurcation and chaos , 2013 .

[15]  W. M. Kusumawinahyu,et al.  Dynamically consistent discrete epidemic model with modified saturated incidence rate , 2013 .

[16]  Yicang Zhou,et al.  Global stability of the endemic equilibrium of a discrete SIR epidemic model , 2013, Advances in difference equations.

[17]  Zhidong Teng,et al.  Stability analysis in a class of discrete SIRS epidemic models , 2012 .

[18]  Zhidong Teng,et al.  Stability and bifurcation analysis of a discrete predator–prey model with nonmonotonic functional response , 2011 .

[19]  Richard L. Magin,et al.  On the fractional signals and systems , 2011, Signal Process..

[20]  Zhimin He,et al.  Bifurcation and chaotic behavior of a discrete-time predator–prey system ☆ , 2011 .

[21]  Junwei Wang,et al.  Chaos Control of a Fractional-Order Financial System , 2010 .

[22]  Benito M. Chen-Charpentier,et al.  A nonstandard numerical scheme of predictor-corrector type for epidemic models , 2010, Comput. Math. Appl..

[23]  Antonia Vecchio,et al.  A General Discrete Time Model of Population Dynamics in the Presence of an Infection , 2009 .

[24]  Elmetwally M. Elabbasy,et al.  Chaotic dynamics of a discrete prey-predator model with Holling type II , 2009 .

[25]  Rafael J. Villanueva,et al.  Nonstandard numerical methods for a mathematical model for influenza disease , 2008, Math. Comput. Simul..

[26]  A. Yakubu,et al.  Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models , 2008, Journal of mathematical biology.

[27]  李建全,et al.  Some discrete SI and SIS epidemic models , 2008 .

[28]  Ronald E Mickens,et al.  Numerical integration of population models satisfying conservation laws: NSFD methods , 2007, Journal of biological dynamics.

[29]  Xianning Liu,et al.  Avian-human influenza epidemic model. , 2007, Mathematical biosciences.

[30]  Dongmei Xiao,et al.  Complex dynamic behaviors of a discrete-time predator–prey system , 2007 .

[31]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[32]  Julien Clinton Sprott,et al.  Chaos in fractional-order autonomous nonlinear systems , 2003 .

[33]  Vicenç Méndez,et al.  Dynamical evolution of discrete epidemic models , 2000 .

[34]  H. Thieme,et al.  Recurrent outbreaks of childhood diseases revisited: the impact of isolation. , 1995, Mathematical biosciences.

[35]  R. Bagley,et al.  The fractional order state equations for the control of viscoelastically damped structures , 1989 .

[36]  M. Ichise,et al.  An analog simulation of non-integer order transfer functions for analysis of electrode processes , 1971 .

[37]  M. Caputo Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[38]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[39]  Jinde Cao,et al.  Bifurcations in a delayed fractional complex-valued neural network , 2017, Appl. Math. Comput..

[40]  Katharina Wagner,et al.  Inners And Stability Of Dynamic Systems , 2016 .

[41]  Tailei Zhang,et al.  Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence , 2015, Appl. Math. Lett..

[42]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[43]  Zhidong Teng,et al.  The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence , 2013 .

[44]  A. El-Sayed,et al.  ON A DISCRETIZATION PROCESS OF FRACTIONAL ORDER RICCATI DIFFERENTIAL EQUATION , 2013 .

[45]  Carlos Castillo-Chavez,et al.  Discrete epidemic models. , 2010, Mathematical biosciences and engineering : MBE.

[46]  Herbert W. Hethcote,et al.  An SIS epidemic model with variable population size and a delay , 1995, Journal of mathematical biology.

[47]  C. Piccardi,et al.  Bifurcation analysis of periodic SEIR and SIR epidemic models , 1994, Journal of mathematical biology.

[48]  J. Heesterbeek,et al.  The saturating contact rate in marriage- and epidemic models , 1993, Journal of mathematical biology.

[49]  Herbert W. Hethcote,et al.  Dynamic models of infectious diseases as regulators of population sizes , 1992, Journal of mathematical biology.

[50]  R. Bagley,et al.  Fractional order state equations for the control of viscoelasticallydamped structures , 1991 .