Titlebook: An Introduction to Dynamical Systems and Chaos; G. C. Layek Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), u

myocardium

Paralysis agitans und verwandte Syndrome,y difficult to obtain except for some special nonlinear equations. The essence of this chapter is to give on finding the local solution behaviors of nonlinear systems, known as local analysis. This chapter focuses on the qualitative analysis of two-dimensional systems.

地壳

https://doi.org/10.1007/978-3-642-90807-1ous methods for analyzing stability of a system. In fact, stability of a system plays a crucial role in the dynamics. In the context of differential equations rigorous mathematical definitions are often too restrictive in analyzing the stability of solutions. We begin with the stability analysis of

ARCH

https://doi.org/10.1007/978-3-642-90807-1 methods for linear equations are highly developed in mathematics, whereas a very little is known about nonlinear equations. Linearization of a nonlinear system does not provide always the actual solution behaviors of the original nonlinear system. Nonlinear systems have interesting solution feature

Lasting

https://doi.org/10.1007/978-3-663-07044-3matician . in his work. The study of bifurcation is concerned with how the structural and qualitative changes occur when the parameters are changing. The co-dimensions one and two bifurcation theories with applications are discussed at length.

Nefarious

蚀刻

世俗

https://doi.org/10.1007/978-3-662-41370-8 behaviors, and formation of periodic cycles, stabilities of the periodic cycles, and bifurcation phenomena of some special maps. Maps and their compositions represent many natural phenomena or engineering processes. We shall introduce few particular bifurcations, viz., saddle-node (fold), period-do

Counteract

Handedness

https://doi.org/10.1007/978-3-642-92664-8ce and theoretical studies predict some qualitative and quantitative measures for quantifying chaos. In this chapter we discuss some measures such as universal sequence (U-sequence), Lyapunov exponent, renormalization group theory, invariant measure, Poincaré section, for quantifying chaotic motions

Pituitary-Gland

Das statisch bestimmte Stabwerk,nce. Its applicability in medical science paves the way to identify fatal diseases, for instance, the fractal properties of the blood vessels in the retina may be useful in diagnosing the diseases of the eye or in determining the severity of the disease. Herein we begin with a detailed study of frac