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67

Sep 18, 2013
09/13

Sep 18, 2013
by
K. B. Blyuss; Y. N. Kyrychko

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Effects of immune delay on symmetric dynamics are investigated within a model of antigenic variation in malaria. Using isotypic decomposition of the phase space, stability problem is reduced to the analysis of a cubic transcendental equation for the eigenvalues. This allows one to identify periodic solutions with different symmetries arising at a Hopf bifurcation. In the case of small immune delay, the boundary of the Hopf bifurcation is found in a closed form in terms of system parameters. For...

Source: http://arxiv.org/abs/1209.4475v1

43
43

Sep 18, 2013
09/13

Sep 18, 2013
by
Y. N. Kyrychko; K. B. Blyuss; E. Schoell

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This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in terms of average frequency, frequency detuning and parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insight into the dynamics inside amplitude death...

Source: http://arxiv.org/abs/1209.0133v1

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49

Sep 18, 2013
09/13

Sep 18, 2013
by
K. B. Blyuss; Y. N. Kyrychko

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An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is...

Source: http://arxiv.org/abs/1201.4587v1

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46

Sep 18, 2013
09/13

Sep 18, 2013
by
Y. N. Kyrychko; K. B. Blyuss; P. Hoevel; E. Schoell

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Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived exact stability boundary. The approximate and exact stability borders agree quite well for the large time delay, and the inclusion of a time-delayed velocity feedback improves this agreement for small delays. Theoretical results are complemented by a numerically...

Source: http://arxiv.org/abs/1201.5957v1

39
39

Sep 18, 2013
09/13

Sep 18, 2013
by
Y. N. Kyrychko; K. B. Blyuss; S. J. Hogan; E. Schoell

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This paper studies the effects of a time-delayed feedback control on the appearance and development of spatiotemporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species, diagonal, and mixed control. This approach helps to unveil different dynamical regimes, which arise from chaotic state or from traveling waves. In the case of spatiotemporal chaos, the control can either stabilize uniform steady states or lead to bistability...

Source: http://arxiv.org/abs/1201.6151v1

50
50

Sep 18, 2013
09/13

Sep 18, 2013
by
K. B. Blyuss; Y. N. Kyrychko; P. Hoevel; E. Schoell

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We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original system parameters and the time delay of the control. Theoretical and numerical results show that the interplay...

Source: http://arxiv.org/abs/1201.5964v1

3
3.0

Jun 28, 2018
06/18

Jun 28, 2018
by
K. Parmar; K. B. Blyuss; Y. N. Kyrychko; S. J. Hogan

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In this review we discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.

Topics: Molecular Networks, Quantitative Biology, Quantitative Methods

Source: http://arxiv.org/abs/1510.08513

2
2.0

Jun 28, 2018
06/18

Jun 28, 2018
by
G. Neofytou; Y. N. Kyrychko; K. B. Blyuss

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In the studies of plant infections, the plant immune response is known to play an essential role. In this paper we derive and analyse a new mathematical model of plant immune response with particular account for post-transcriptional gene silencing (PTGS). Besides biologically accurate representation of the PTGS dynamics, the model explicitly includes two time delays to represent the maturation time of the growing plant tissue and the non-instantaneous nature of the PTGS. Through analytical and...

Topics: Quantitative Biology, Chaotic Dynamics, Quantitative Methods, Nonlinear Sciences

Source: http://arxiv.org/abs/1511.05475

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4.0

Jun 29, 2018
06/18

Jun 29, 2018
by
G. Neofytou; Y. N. Kyrychko; K. B. Blyuss

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Cross-protection, which refers to a process whereby artificially inoculating a plant with a mild strain provides protection against a more aggressive isolate of the virus, is known to be an effective tool of disease control in plants. In this paper we derive and analyse a new mathematical model of the interactions between two competing viruses with particular account for RNA interference. Our results show that co-infection of the host can either increase or decrease the potency of individual...

Topics: Quantitative Biology, Quantitative Methods, Chaotic Dynamics, Nonlinear Sciences, Populations and...

Source: http://arxiv.org/abs/1612.01561

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8.0

Jun 30, 2018
06/18

Jun 30, 2018
by
Y. N. Kyrychko; K. B. Blyuss; E. Schoell

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This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distributed delay coupling can be determined through a semi-analytic computation of Floquet exponents. The analysis of stability of fully synchronized and of...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1406.5428

2
2.0

Jun 30, 2018
06/18

Jun 30, 2018
by
G. O. Agaba; Y. N. Kyrychko; K. B. Blyuss

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This paper analyses an SIRS-type model for infectious diseases with account for behavioural changes associated with the simultaneous spread of awareness in the population. Two types of awareness are included into the model: private awareness associated with direct contacts between unaware and aware populations, and public information campaign. Stability analysis of different steady states in the model provides information about potential spread of disease in a population, and well as about how...

Topics: Populations and Evolution, Quantitative Biology, Chaotic Dynamics, Nonlinear Sciences, Quantitative...

Source: http://arxiv.org/abs/1702.04999

3
3.0

Jun 30, 2018
06/18

Jun 30, 2018
by
G. O. Agaba; Y. N. Kyrychko; K. B. Blyuss

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This paper analyses the dynamics of infectious disease with a concurrent spread of disease awareness. The model includes local awareness due to contacts with aware individuals, as well as global awareness due to reported cases of infection and awareness campaigns. We investigate the effects of time delay in response of unaware individuals to available information on the epidemic dynamics by establishing conditions for the Hopf bifurcation of the endemic steady state of the model. Analytical...

Topics: Populations and Evolution, Quantitative Biology, Chaotic Dynamics, Nonlinear Sciences, Quantitative...

Source: http://arxiv.org/abs/1704.05912