We analyze the dynamics of the forced singularly perturbed differential equations of Duffing’s type with a potential that is bounded from above. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled by a small parameter at the highest derivative.

In paper we analyze the high sensitivity of solutions to nonlinear singularly perturbed second-order dynamical systems on the initial conditions and the value of singular parameter at highest derivative of the mathematical model. Analyzing the potential profile of the system we study the oscillation patterns occurring in the system. The theory is illustrated by numerical simulation.

In this paper, the method for determining of turning point location of concave solutions for some class of singularly perturbed nonlinear differential equations subject to the Dirichlet boundary conditions is proposed.

Singularly Perturbed Linear Neumann Problem with the Characteristic Roots on the Imaginary Axis We investigate the problem of existence and asymptotic behavior of solutions for the singularly perturbed linear Neumann problem <img src="/fulltext-image.asp?format=htmlnonpaginated&src=C6551P41673P4147_html\Journal10186_Volume18_Issue28_20_paper.gif" alt=""/> Our approach relies on the analysis of integral equation equivalent to the problem above.

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