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This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem…
We derive a necessary and sufficient condition for Turing instabilities to occur in two-component systems of reaction-diffusion equations with Neumann boundary conditions. We apply this condition to reaction-diffusion systems built from…
The iron-based superconductors allow for a zoo of possible order parameters due to their orbital degrees of freedom. These order parameters are often written in an orbital basis, as this allows to distinguish their different symmetry.…
A Hopf bifurcation in the Kuramoto-Daido model is investigated based on the generalized spectral theory and the center manifold reduction for a certain class of frequency distributions. The dynamical system of the order parameter on a…
We consider a broad class of second-order dynamical systems and study the impact of damping as a system parameter on the stability, hyperbolicity, and bifurcation in such systems. We prove a monotonic effect of damping on the hyperbolicity…
The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the…
We carried out a fluid dynamical simulation for a forced dripping faucet system using a new algorithm that was recently developed. The simulation shows that periodic external forcing induces transitions from chaotic to periodic motion and…
This paper presents a general framework to derive the weakly nonlinear stability near a Hopf bifurcation in a special class of multi-scale reaction-diffusion equations. The main focus is on how the linearity and nonlinearity of the fast…
The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
Real power systems exhibit dynamics that evolve across a wide range of time scales, from very fast to very slow phenomena. Historically, incorporating these wide-ranging dynamics into a single model has been impractical. As a result, power…
We conduct a local stability and Hopf bifurcation analysis for Compound TCP, with small Drop-tail buffers, in three topologies. The first topology consists of two sets of TCP flows having different round trip times, and feeding into a core…
We study the existence of asymptotically stable periodic trajectories induced by reset feedback. The analysis is developed for a planar system. Casting the problem into the hybrid setting, we show that a periodic orbit arises from the…
For piecewise-smooth ordinary differential equations, the occurrence of a Hopf bifurcation on a switching surface is known as a boundary Hopf bifurcation. Boundary Hopf bifurcations are codimension-two, so occur at points in two-parameter…
This paper is about the existence of periodic orbits near an equilibrium point of a two-degree-of-freedom Hamiltonian system. The equilibrium is supposed to be a nondegenerate minimum of the Hamiltonian. Every sphere-like component of the…
In this paper we analyze a simple mathematical model which describes the interaction between the proteins p53 and Mdm2. For the stationary state we discuss the local stability and the existence of the Hopf bifurcation. Choosing the delay as…
Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a…
In this paper we analyse a dynamical system based on the so-called KCG (K\"all\'en, Crafoord, Ghil) conceptual climate model. This model describes an evolution of the globally averaged temperature and the average extent of the ice sheets.…
This paper investigates equilibrium points and stability in two synchronous machine configurations: (i) a single generator with an impedance load and (ii) two interconnected machines with co-located loads. We consider both abc and dq…
A general FitzHugh-Rinzel model, able to describe several neuronal phenomena, is considered. Linear stability and Hopf bifurcations are investigated by means of the spectral equation for the ternary autonomous dynamical system and the…