Browsing by Author "Braverman, E."

Now showing 1 - 3 of 3
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    On a Difference Equation with Exponentially Decreasing Nonlinearity
    (Hindawi Publishing Corporation, 2011-06-01) Braverman, E.; Saker, S. H.
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    On a Difference Equation with Exponentially Decreasing Nonlinearity
    (2011-07-28) Braverman, E.; Saker, S. H.
    We establish a necessary and sufficient condition for global stabilityof the nonlinear discrete red blood cells survival model and demonstrate that local asymptoticstability implies global stability. Oscillation and solution bounds are investigated. We also showthat, for different values of the parameters, the solution exhibits some time-varying dynamics, that is,if the system is moved in a direction away from stability (by increasing the parameters), thenit undergoes a series of bifurcations that leads to increasingly long periodic cycles and finally todeterministic chaos. We also study the chaotic behavior of the model with a constant positiveperturbation and prove that, for large enough values of one of the parameters, the perturbed systemis again stable.
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    On Nonoscillation of Advanced Differential Equations with Several Terms
    (2011-03-30) Berezansky, L.; Braverman, E.
    Existence of positive solutions for advanced equations with several terms is investigated in the following three cases: (a) all coefficients are positive; (b) all coefficients are negative; (c) there is an equal number of positive and negative coefficients. Results on asymptotics of nonoscillatory solutions are also presented.