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Collision of equilibria with a splitting manifold has been locally studied, but might also be a contributing factor to global bifurcations. In particular a boundary collision can be coincident with collision of a virtual equilibrium with a…
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddle-node, pitchfork or Hopf…
For an elastic system that is non-conservative but autonomous, subjected for example to time-independent loading by a steadily flowing fluid (air or water), a dangerous bifurcation, such as a sub-critical bifurcation, or a cyclic fold, will…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction 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…
In aggregation-fragmentation processes, a steady state is usually reached in the long time limit. This indicates the existence of a fixed point in the underlying system of ordinary differential equations. The next simplest possibility is an…
We study the linear instabilities and bifurcations in the Selkov model for glycolysis with diffusion. We show that this model has a zero wave-vector, finite frequency Hopf bifurcation to a growing oscillatory but spatially homogeneous state…
Standard geometric control relies on force-moment decoupling, an assumption that breaks down in many aerial platforms due to spurious forces naturally induced by control moments. While strategies for such coupled systems have been validated…
The appearance of travelling-wave-type solutions in pipe Poiseuille flow that are disconnected from the basic parabolic profile is numerically studied in detail. We focus on solutions in the 2-fold azimuthally-periodic subspace because of…
A normal form is derived for Hamiltonian-Hopf bifurcations of solitary waves in generalized nonlinear Schr\"odinger equations. This normal form is a simple second-order nonlinear ordinary differential equation that is asymptotically…
Elastic strips provide a canonical system for studying the mechanisms governing elastic shape transitions. Buckling, linear snap-through, and nonlinear snap-through have been observed in boundary-actuated strips and linked to the type of…
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…
Self-excited limit-cycle oscillations (LCOs) from Hopf bifurcations are a key feature of nonlinear aeroelasticity and depend sensitively on structural and aerodynamic parameters. Classical center-manifold and normal-form theory describe…
In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications…
Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast-slow stochastic…
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to…
We develop a global bifurcation theory for two classes of nonlinear elastic materials. It is supposed that they are subjected to anti-plane shear deformation and occupy an infinite cylinder in the reference configuration. Curves of…
We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model,…
This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…
The double Hamiltonian Hopf bifurcation is studied, i.e. a generic two-parametric unfolding of a smooth Hamiltonian system with four degrees of freedom which has at the critical value of parameters the equilibrium with two pairs of double…