Global Analysis and the Periodic Character of a Class of Difference Equations

In biology, difference equations is often used to understand and describe life phenomenon through mathematical models. So, in this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. Furthermore, this equation involves a May’s Host Parasitoid Model, as a special case.

[1]  E. Camouzis,et al.  Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures , 2001 .

[2]  Stevo Stević,et al.  On the recursive sequence $$x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}$$ , 2005 .

[3]  E. M. Elsayed,et al.  On a max-type and a min-type difference equation , 2009, Appl. Math. Comput..

[4]  Wen-Xiu Ma.  Global Behavior of a New Rational Nonlinear Higher-Order Difference Equation , 2019, Complex..

[5]  Elsayed M. Elsayed,et al.  New method to obtain periodic solutions of period two and three of a rational difference equation , 2015 .

[6]  Stevo Stević,et al.  Global stability and asymptotics of some classes of rational difference equations , 2006 .

[7]  E. Elabbasy,et al.  Dynamics of a rational difference equation , 2009 .

[8]  Ravi P. Agarwal,et al.  Almost periodic solution for a new type of neutral impulsive stochastic Lasota-Wazewska timescale model , 2017, Appl. Math. Lett..

[9]  Andrei Pogrebkov,et al.  Hirota Difference Equation and Darboux System: Mutual Symmetry , 2019, Symmetry.

[10]  G. Ladas,et al.  Periodicities in Nonlinear Difference Equations , 2004 .

[11]  Stevo Stevic,et al.  Existence of nontrivial solutions of a rational difference equation , 2007, Appl. Math. Lett..

[12]  On the Recursive Sequence , 2003 .

[13]  Xiuxiang Liu,et al.  A note on the existence of periodic solutions in discrete predator–prey models ☆ , 2010 .

[14]  Stevo Stević,et al.  Asymptotics of Some Classes of Higher-Order Difference Equations , 2007 .

[15]  Chen Yang,et al.  Positive Solutions for a Three-Point Boundary Value Problem of Fractional Q-Difference Equations , 2018, Symmetry.

[16]  Osama Moaaz,et al.  Dynamics of difference equation xn+1=f(xn−l,xn−k)$x_{n+1}=f( x_{n-l},x_{n-k})$ , 2018, Advances in Difference Equations.

[17]  Osama Moaaz,et al.  Comment on “New method to obtain periodic solutions of period two and three of a rational difference equation” [Nonlinear Dyn 79:241–250] , 2017 .

[18]  Stevo Stević,et al.  On the Recursive Sequence xn=1 , 2007 .

[19]  J. Andres,et al.  Limit-Periodic Solutions of the Difference Equation x t + 1 − , 2019 .

[20]  Stevo Stević.  Short Note: A Note on Periodic Character of a Difference Equation , 2004 .

[21]  Michael Gil,et al.  Solution Estimates for the Discrete Lyapunov Equation in a Hilbert Space and Applications to Difference Equations , 2019, Axioms.

[22]  A. Peterson,et al.  Difference Equations: An Introduction with Applications , 2000 .

[23]  H. El-Metwally,et al.  On a System of Difference Equations of an Economic Model , 2013 .

[24]  V. Kocić,et al.  Global Behavior of Nonlinear Difference Equations of Higher Order with Applications , 1993 .

[25]  Osama Moaaz,et al.  Some Qualitative Behavior of Solutions of General Class of Difference Equations , 2019, Mathematics.

[26]  Shair Ahmad,et al.  On the nonautonomous Volterra-Lotka competition equations , 1993 .

[27]  Qamar Din,et al.  Stability analysis of a discrete ecological model , 2014 .

[28]  K. Tomsovic,et al.  Stability analysis of a class of switched nonlinear systems using the time scale theory , 2019, Nonlinear Analysis: Hybrid Systems.

[29]  James V. Rauff.  Mathematical Models in Biology: An Introduction , 2005 .

[30]  Stevo Stević,et al.  A short proof of the Cushing-Henson conjecture , 2006 .

[31]  Kenneth S. Berenhaut,et al.  A note on positive non-oscillatory solutions of the difference equation , 2006 .

[32]  Janusz Migda,et al.  Nonoscillatory Solutions to Second-Order Neutral Difference Equations , 2018, Symmetry.

[33]  Sophie Papst.  Discrete Hamiltonian Systems Difference Equations Continued Fractions And Riccati Equations , 2016 .

[34]  Wolfram Koepf,et al.  On Solutions of Holonomic Divided-Difference Equations on Nonuniform Lattices , 2013, Axioms.

[35]  M. M. el-Dessoky,et al.  Dynamics and behavior of a higher order rational recursive sequence , 2012 .

[36]  E. Elsayed.  Dynamics and behavior of a higher order rational difference equation , 2016 .

[37]  S. Stević.  Asymptotic Periodicity of a Higher-Order Difference Equation , 2007 .

[38]  Mama Foupouagnigni,et al.  On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices , 2019, Axioms.