Hopf bifurcation in symmetric systems
Hopf bifurcation in the IS-LM business cycle model with time delay.
Hopf bifurcation of a mathematical model for growth of tumors with an action of inhibitor and two time delays.
Hopf bifurcation of integro-differential equations.
Hopf bifurcation with -symmetry.
Hopf-bifurcation in systems with spherical symmetry. I: Invariant tori.
Hopf-bifurcation in systems with spherical symmetry, Part II: Connecting orbits.
Hopf's ratio ergodic theorem by inducing
We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.
Horoballs in simplices and Minkowski spaces.
Horospheres and the Stable Part of the Geodesic Flow.
Horseshoe in a class of planar mappings.
How and why do neurons generate complex rhythms with various frequencies?
How complicated can be one-dimensional dynamical systems: descriptive estimates of sets
Hubbard trees
We provide a full classification of postcritically finite polynomials as dynamical systems by means of Hubbard trees. The information encoded in these objects is solid enough to allow us recover all the relevant statical and dynamical aspects of the corresponding Julia sets.
Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling
HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic mechanisms are manifold and mediated through a range of positive and negative feedback regulations of immune and physiological processes engaged in virus-host interactions. The fundamental questions towards understanding the pathogenesis of HIV infection are now shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally disrupted? (ii)...
Hybrid matrix models and their population dynamic consequences
In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as well...
Hybrid matrix models and their population dynamic consequences
In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as...
Hyperbolic characteristics on star-shaped hypersurfaces
Hyperbolic components of polynomials with a fixed critical point of maximal order
Hyperbolic components of the complex exponential family
We describe the structure of the hyperbolic components of the parameter plane of the complex exponential family, as started in [1]. More precisely, we label each component with a parameter plane kneading sequence, and we prove the existence of a hyperbolic component for any given such sequence. We also compare these sequences with the more commonly used dynamical kneading sequences.