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- 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
- 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)

- 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). Delay… (More)

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

Abstract. In this paper we describe a method for continuing periodic solution bifurcations in periodic delaydifferential 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… (More)

- Robert 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)

- Robert Szalai, Hinke M. Osinga
- Chaos
- 2008

The paper investigates generic three-dimensional nonsmooth systems with a periodic orbit near grazing-sliding. We assume that the periodic orbit is unstable with complex multipliers so that two dominant frequencies are present in the system. Because grazing-sliding induces a dimension loss and the instability drives every trajectory into sliding, the system… (More)

- Robert Szalai, Alan R. Champneys, Martin E. Homer, Dáibhid Ó Maoiléidigh, Helen Kennedy, N. R. Cooper
- The Journal of the Acoustical Society of America
- 2013

Various simple mathematical models of the dynamics of the organ of Corti in the mammalian cochlea are analyzed and their dynamics compared. The specific models considered are phenomenological Hopf and cusp normal forms, a recently proposed description combining active hair-bundle motility and somatic motility, a reduction thereof, and finally a model… (More)

- Robert Szalai, Krasimira Tsaneva-Atanasova, Martin E. Homer, Alan R. Champneys, Helen Kennedy, Nigel 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)

- Gábor Orosz, R. Eddie Wilson, Robert 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)

Introduction In today’s fast-paced, connected world the effects of a single business or policy decision may quickly cascade through a number of hidden links and affect remote parts of the market or the organization. To cope with such difficulties decision-makers need novel tools. This is the reason why modeling and simulation applications play an increasing… (More)