On a modification of a discrete epidemic model

Stability of two 3 × 3 close‐to‐cyclic systems of exponential difference equations

“…(3) where a 1 , a 2 , a 3 , b 1 , b 2 , and b 3 are real numbers and the initial values are real numbers. Assume that (8) and (9) hold and…”

“…So a large number of papers dealing with such equations have been published. Some of them can be found in previous studies . The most interesting special cases of such equations are usually those whose characteristic polynomials of their linearizations have characteristic zeros belonging to the unit circle.…”

“…We would like to point out that some of these papers study even some more general systems of difference equations which are nowadays frequently called close‐to‐cyclic (for the case of two‐dimensional system they are called close‐to‐symmetric, see, for example, other works). For some results on symmetric and close‐to‐symmetric systems, which are nowadays popular, see previous studies and the references therein. Finally, since difference equations have several applications in applied sciences, there exists an extended bibliography concerning theory and applications (see other works ),.…”

“…Some of them can be found in previous studies. [1][2][3][4][5][6][7][8][9] The most interesting special cases of such equations are usually those whose characteristic polynomials of their linearizations have characteristic zeros belonging to the unit circle. Some classical results in this direction can be found in Carr 10 and Kuznetsov.…”

Stability of the Non-Hyperbolic Zero Equilibrium of Two Close-to-Symmetric Systems of Difference Equations with Exponential Terms

“…There has been interest in difference equations of biological models for a long period of time. Some of the research can be found in [1][2][3][4][5][6][7][8]. The most interesting special cases of such equations are usually those whose characteristic polynomials of their linearizations have characteristic zeros belonging to the unit circle.…”