Linear system theory provides an inadequate characterization of sustained oscillation in nature. In this two-part exposition of oscillation in piecewise-linear dynamical systems, we guide the reader from linear concepts and simple harmonic motion to nonlinear concepts and chaos. By means of three worked examples, we bridge the gap from the familiar parallel RLC network to exotic nonlinear dynam...

The photochemical system of the mesopause region is a nonlinear driven oscillator enforced by the diurnal-periodic solar radiation. Under idealized conditions this oscillator can display nonlinear effects such as period doubling cascades or chaos. We investigate what happens if this system is subjected to atmospheric diffusion. A highresolution one-dimensional chemical system of the mesopause r...

This paper is concerned with the oscillatory behavior of the fourth-order nonlinear differential equation (E) (p(t)|x| x)′′ + q(t)|x|x = 0 , where α > 0, β > 0 are constants and p, q : [a,∞) → (0,∞) are continuous functions satisfying conditions

In this paper, an analytical technique has been developed based on a modified harmonic balance method to determine higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term, is an anti-symmetric and quadratic term. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these al...

Using generalized Riccati transformations, we derive new interval oscillation criteria for a class of general type second-order nonlinear differential equations with nonlinear damping. Examples are also given to illustrate the results. 2000 Mathematics Subject Classification: 34C10

Our aim in this paper is to present criteria for oscillation of the nonlinear differential equation u′′(t) + p(t)f `

This paper deals with oscillation criteria for even order nonlinear neutral mixed type differential equations of the form

performance measure approach (pma) is a method for evaluating the probabilistic constraints in reliability-based design optimization of structures. the advanced mean-value (amv) method is suitable for pma, simply and efficiently. the iterative amv scheme could be yielded to unstable solutions such as periodic-oscillation and chaos for highly nonlinear performance functions. in the present paper...