A planar ODE system which models the industrialization of a small open economy is considered. Because fractional powers are involved, its interior equilibria hardly found by solving transcendental equation and routine qualitative analysis not applicable. We qualitatively discuss equation, eliminating term to polynomialize expression extreme value, so that we can compute polynomials obtain numbe...

To each complex semisimple Lie algebra $$ \mathfrak{g} and regular element a ∈ reg, one associates Mishchenko–Fomenko subalgebra \mathcal{F} ⊆ ℂ[ ]. This amounts to completely integrable system on the Poisson variety , as such has bifurcation diagram Σa Spec( a). We prove that codimension in a) if reg is not nilpotent, it or two nilpotent. In nilpotent case, we show of possible codimensions be ...

A problem of frequent interest in the analysis of nonlinear ODE systems is the location of equilibrium states and bifurcations. Through the use of bifurcation diagrams, a large amount of information concerning the number and stability of equilibria in an ODE model can be concisely represented. Bifurcations of equilibria are typically found by solving a nonlinear algebraic system consisting of t...

We discuss new and improved algorithms for the bifurcation analysis of fixed points and periodic orbits (cycles) of maps and their implementation in matcont, a matlab toolbox for continuation and bifurcation analysis of dynamical systems. This includes the numerical continuation of fixed points of iterates of the map with one control parameter, detecting and locating their bifurcation points (i...

One of the possible consequences of global warming in the northern hemisphere is the invasion of Arctic Tundra by woody plants, which is influenced by the chemical defense of plants against mammal browsing. In this paper, we explore the toxin-mediated plant-herbivore interaction with size structure in plants using a simplified mathematical model. The size structure of plants is important as it ...

Bosch Vivancos, Chossat and Melbourne showed that two types of steadystate bifurcations are possible from trivial states when Euclidean equivariant systems are restricted to a planar lattice—scalar and pseudoscalar—and began the study of pseudoscalar bifurcations. The scalar bifurcations have been well studied since they appear in planar reaction–diffusion systems and in plane layer convection ...

In this paper, we consider a general reaction-diffusion system with nonlocal effects and Neumann boundary conditions, where spatial average kernel is chosen to be the kernel. By virtue of center manifold reduction technique normal form theory, present new algorithm for computing forms associated codimension-two double Hopf bifurcation. The theoretical results are applied predator-prey model, co...