On a codimension three bifurcation
We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in...
The author considers the quasilinear differential equations By means of topological tools there are established conditions ensuring the existence of nonnegative asymptotic decaying solutions of these equations.
The paper describes asymptotic properties of a strongly nonlinear system , . The existence of an parametric family of solutions tending to zero is proved. Conditions posed on the system try to be independent of its linear approximation.
In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.
We study the connection between the entropy of a dynamical system and the boundary distortion rate of regions in the phase space of the system.