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- Róbert Szalai, Gábor Stépán, S John Hogan
- Chaos
- 2004

In the case of low immersion high-speed milling, the ratio of time spent cutting to not cutting can be considered as a small parameter. In this case the classical regenerative vibration model of machine tool vibrations reduces to a simplified discrete mathematical model. The corresponding stability charts contain stability boundaries related to period… (More)

- Serafim Rodrigues, David Barton, Robert Szalai, Oscar Benjamin, Mark P. Richardson, John R. Terry
- Journal of Computational Neuroscience
- 2009

In this paper we present a detailed theoretical analysis of the onset of spike-wave activity in a model of human electroencephalogram (EEG) activity, relating this to clinical recordings from patients with absence seizures. We present a complete explanation of the transition from inter-ictal activity to spike and wave using a combination of bifurcation… (More)

- Robert Szalai, Gábor Stépán, Stephen John Hogan
- SIAM J. Scientific Computing
- 2006

In this paper we describe a method for continuing periodic solution bifurcations in periodic delay-differential equations. First, the notion of characteristic matrices of periodic orbits is introduced and equivalence with the monodromy operator is proved. An alternative formulation of the characteristic matrix is given, which can efficiently be computed.… (More)

- Dirk Roose, Koen Engelborghs, Tatyana Luzyanina, Koen Verheyden, Giovanni Samaey, Robert Szalai
- 2010

because they did the work ... 2 Overview • Lecture 1 – numerical methods for delay differential equations (DDEs) with constant pointwise delays • stability analysis of steady state solutions – short introduction to software package DDE-BIFTOOL • Practical session – Demo & hands-on experience with DDE-BIFTOOL 3 Overview (2) • Lecture 2 – computation &… (More)

- Dirk Roose, Robert Szalai
- 2007

Mathematical modeling with delay differential equations (DDEs) is widely used in various application areas of science and engineering (e.g., in semiconductor lasers with delayed feedback, high-speed machining, communication networks, and control systems) and in the life sciences (e.g., in population dynamics , epidemiology, immunology, and physiology).… (More)

- Gábor Orosz, R Eddie Wilson, Róbert Szalai, Gábor Stépán
- Physical review. E, Statistical, nonlinear, and…
- 2009

A nonlinear car-following model is studied with driver reaction time delay by using state-of-the-art numerical continuations techniques. These allow us to unveil the detailed microscopic dynamics as well as to extract macroscopic properties of traffic flow. Parameter domains are determined where the uniform flow equilibrium is stable but sufficiently large… (More)

- László Gulyás, Sándor Bartha, Tamás Kozsik, Róbert Szalai, Attila Korompai, Gábor Tatai
- 2005

- Robert Szalai, Hinke M. Osinga
- SIAM J. Applied Dynamical Systems
- 2009

The Ne˘ ımark-Sacker bifurcation, or Hopf bifurcation for maps, is a well-known bifurcation for smooth dynamical systems. At a Ne˘ ımark-Sacker bifurcation a periodic orbit loses stability and, except for certain so-called strong resonances, an invariant torus is born; the dynamics on the torus can be either quasi-periodic or phase locked, which is… (More)

- R Szalai, K Tsaneva-Atanasova, M E Homer, A R Champneys, H J Kennedy, N P Cooper
- Philosophical transactions. Series A…
- 2011

This paper reviews current understanding and presents new results on some of the nonlinear processes that underlie the function of the mammalian cochlea. These processes occur within mechano-sensory hair cells that form part of the organ of Corti. After a general overview of cochlear physiology, mathematical modelling results are presented in three parts.… (More)

- Róbert Szalai, Gábor Orosz
- Physical review. E, Statistical, nonlinear, and…
- 2013

Delay-coupled networks are investigated with nonidentical delay times and the effects of such heterogeneity on the emergent dynamics of complex systems are characterized. A simple decomposition method is presented that decouples the dynamics of the network into node-size modal equations in the vicinity of equilibria. The resulting independent components… (More)