Related papers: Twenty Hopf-like bifurcations in piecewise-smooth …
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we…
We study a model for a dilute suspension of rod-like particles swimming at constant velocity in a Stokes flow. As the translational diffusivity of the particles decreases, a two-dimensional uniform concentration of randomly aligned…
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…
This paper presents an analysis on nonstandard generalized Hopf bifurcation in a class of switched systems where the lost of stability of linearized systems is not due to the crossing of their complex conjugate eigenvalues but relevant to…
The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…
We study Hopf-Andronov bifurcations in a class of random differential equations (RDEs) with bounded noise. We observe that when an ordinary differential equation that undergoes a Hopf bifurcation is subjected to bounded noise then the…
Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in…
Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated to systems, which drift slowly towards a bifurcation point. In the context of…
On base of Hamiltonian formalism, we show that Hopf bifurcation arrives, in the course of the system evolution, at creation of revolving region of the phase plane being bounded by limit cycle. A revolving phase plane with a set of limit…
The objective of this paper is to study the dynamical behaviour systematically of an ecological system with Beddington-DeAngelis functional response which avoids the criticism occurred in the case of ratio-dependent functional response at…
Inspired by an example of Grebogi et al [1], we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold [2]. The specific structure of these models allows a…
One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described…
The aim of this work is to investigate the qualitative behaviour of a financial dynamical system which contains a time delay. We investigate the dynamic response of this system of which variables are interest rate, investment demand, price…
A data-driven model identification strategy is developed for dynamical systems near a supercritical Hopf bifurcation with nonautonomous inputs. This strategy draws on phase-amplitude reduction techniques, leveraging an analytical…
We discuss tipping phenomena (critical transitions) in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp.…
We state two sufficient criteria for periodic oscillations in mass action systems. Neither criterion requires a computation of the Hurwitz determinants. Instead, both criteria exploit the linear algebra concepts of $D$-stability and…
The equivariant Hopf bifurcation dynamics of a class of system of partial differential equations is carefully studied. The connections between the current dynamics and fundamental concepts in hyperbolic conservation laws are explained. The…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
The cyclicity problem, crucial in analyzing planar vector fields, consists in estimating the number of limit cycles emanating from monodromic singularities. Traditionally, this estimation relies on Lyapunov coefficients. However, in…