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Base-flow computations and stability analyses are performed for a hypersonic wind tunnel nozzle at a Mach number of 6. Isothermal and adiabatic wall boundary conditions are investigated, and moderate stagnation conditions are used to…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
A symmetry breaking mechanism is shown to occur in an array composed of symmetric bistable Lorenz units coupled through a nearest neighbour scheme. When the coupling is increased, we observe the route: standing --> oscillating -->…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
Convection in an infinite fluid layer is often modelled by considering a finite box with periodic boundary conditions in the two horizontal directions. The translational invariance of the problem implies that any solution can be translated…
The motionless conducting state of liquid metal convection with an applied vertical magnetic field confined in a vessel with insulating side walls becomes linearly unstable to wall modes through a supercritical pitchfork bifurcation.…
Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to…
Effects of a coupling between the mechanical vibrations of a quantum dot placed between the two leads of a single electron transistor and coherent tunneling of electrons through a single level in the dot has been studied. We have found that…
We theoretically study divergent fluctuations of dynamical events at non-ergodic transitions. We first focus on the finding that a non-ergodic transition can be described as a saddle connection bifurcation of an order parameter for a time…
The first stages of the path instability phenomenon known to affect the buoyancy-driven motion of gas bubbles rising in weakly or moderately viscous liquids are examined thanks to a recently developed numerical tool designed to assess the…
This article deals with stabilizing discrete-time switched linear systems. Our contributions are threefold: Firstly, given a family of linear systems possibly containing unstable dynamics, we propose a large class of switching signals that…
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows…
We consider noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
We study bifurcation behavior in periodic perturbations of two-dimensional symmetric systems exhibiting codimension-two bifurcations with a double eigenvalue when the frequencies of the perturbation terms are small. We transform the…
Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics and streamline various processes in complex networks. In this…
An autonomous system of ordinary differential equations in the plane with a centre-saddle bifurcation is considered. The influence of time damped perturbations with power-law asymptotics is investigated. The particular solutions tending at…
A switching dynamical system by means of piecewise linear systems in R^3 that presents multistability is presented. The flow of the system displays multiple scroll attractors due to the unstable hyperbolic focus-saddle equilibria with…
We consider the Ricker model with delay and constant or periodic stocking. We found that the high stocking density tends to neutralize the delay effect on stability. Conditions are established on the parameters to ensure the global…
We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of…