Numerical Methods in Dynamical Systems

Dear Colleagues,

The task of generalizing and studying classical and newer differential models appearing in the literature in recent years is always relevant.

This requires the use and development of specialized numerical methods applicable to the study of specific nonlinear dynamical systems.

We mention, for example, the current tasks of conducting qualitative numerical analysis and generating appropriate iterative methods for studying the dynamics of the following:

• Modified micro-electromechanical oscillators;
• Extended Duffing–van der Pol oscillators;
• Generalized anharmonic oscillators;
• Piecewise smooth oscillators;
• Perturbed Morse-type oscillators;
• Modified planar Kelvin–Stuart models;
• Multiple sine-Gordon models;
• Numerical solutions of the Boussinesq equation.

In several cases in the process of calculating the Melnikov functions, researchers find that the expressions of the Melnikov functions cannot be solved analytically because the homo/heteroclinic orbits are very complex. For this purpose, numerical algorithms are usually proposed and used in practice.

Another interesting possibility is the use of high-order Melnikov polynomials to generate antenna factors. This requires the use of specific numerical algorithms from the fields of approximation theory and optimization theory.

Prof. Dr. Nikolay Kyurkchiev
Prof. Dr. Anton Iliev
Guest Editors

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