In this review article, we present in some detail new trends in application of asymptotic
techniques to mechanical problems. First we consider the various methods which allows for …

Complex networks have been extensively investigated in recent years. However, the
dynamics, especially chaos and bifurcation, of the complex-valued complex network are …

In this book a detailed and systematic treatment of asymptotic methods in the theory of plates
and shells is presented. The main features of the book are the basic principles of …

In this paper, the analytical methods for approximate solutions of periodic motions to chaos
in nonlinear dynamical systems are reviewed. Briefly discussed are the traditional analytical …

Time delays are many sources of complex behavior in dynamical systems. Yet its
relationship with bursting dynamics needs to be further explored, particularly when the …

In this paper, we study the classical Van der Pol's equation with delayed feedback. We
investigate the Bogdanov–Takens singularity and bifurcation occurring in the system with …

This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic
balance method. To investigate a non-linearity in the damping term, the system chosen for …

Abstract The (3+ 1)-dimensional Geng equation is an extended version of the KdV model
that describes the wave dynamics behavior of shallow water waves in complex applications …

Approximate, analytical solutions of period-m motions in a periodically forced, van der Pol
oscillator are obtained through the Fourier series expression, and the corresponding stability …

In this paper, independent, symmetric, periodic motions in a van der Pol oscillator are
predicted through a semi-analytical method. This semi-analytic method is based on the …