interactively available and provides computational and visualization tools. matcont uses the Matlab symbolic toolbox whenever it is available; higher order derivatives are important e.g. in the computation of normal forms. The sparsity of the discretized systems for the computation of limit cycles

of codim 1 and 2, the critical normal form coefficients are computed, both numerically with finite directional differences and using symbolic derivatives of the original map. Using a parameter-dependent center manifold reduction, explicit asymptotics are derived for bifurcation curves of double

Stability analysis algorithms coupled with a robust Newton-Krylov steady state iterative solver are used to understand the behavior of the 2D model problem of thermal convection in a 8:1 differentially heated cavity. Parameter continuation methods along with bifurcation and linear stability

predator-prey systems: Spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations

-critical codimension-two point with a triple +1-Floquet multiplier. The weakly nonlinear analysis of the dynamics near such point is performed by deriving a system of amplitude equations us-ing a perturbation technique, which is an extension of the Lindstedt-Poincaré method, and solvability conditions. The results

to stable attractors called invariant closed curves, and chaos, where dynamics of the system change erratically. Our study is based on the numerical continuation method under variation of 1 and 2 parameters and computation of dierent bifurcation curves of the system and its iterations. For the all

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution

that using d = 2 choices yields an exponential improvement in the expected time a customer spends in the system over d = 1 choice (simple random selection) in equilibrium. Here we examine several variations, including constant service times and threshold models, where a customer makes up to d successive

Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations

. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times. I.