It is rigorously proven under certain assumptions that a quasilinear system with
discontinuous right-hand side possesses a unique unpredictable solution. The …

The present chapter is one of the core parts of this book. It combines the existence of
continuous almost periodic solutions which appear in the special way (the cascade of almost …

The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well
as rate of convergence and transversal manifolds are not under discussion, and the …

In the present paper, an essential generalization of the symbolic dynamics is considered.
We apply the notions of abstract self-similar sets and the similarity map for a chaos …

In this chapter, we consider linear quaternion-valued ordinary differential equations (QDEs)
with impulses at fixed times. We consider linear homogeneous and nonhomogeneous …

It is rigorously proved under certain assumptions that a quasilinear system with
discontinuous right-hand side possesses a unique unpredictable solution. The …

It is rigorously proved that a Li-Yorke chaotic perturbation of a system with a homoclinic orbit
creates chaos along each periodic trajectory. The structure of the chaos is investigated, and …

This chapter is of big interest to those readers, who look for three subjects of investigation:
neural networks theory; nonlinear oscillations; and development of results for discontinuous …