Hierarchy and Polysynchrony in an adaptive network

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be non-trivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: nodes can be divided in differently synchronized classes but contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behaviour can evolve from undifferentiated nodes.Comment: 13 pages, 17 figure

Individual Budgets : Lessons from Early Users' Experiences

Within the context of modernization, there has been a trend towards 'cash-for-care' schemes designed to bring choice and control closer to the service user. In England, Individual Budgets (IBs) are being piloted, with the aim of promoting personalized support for disabled people and other users of social care services. This paper reports on the experiences and outcomes of early IB users two to three months after first being offered an IB. The users included adults with physical/sensory impairments, learning difficulties, mental health problems and older people. Semi-structured interviews were carried out with nine service users and five proxies. The findings suggest that IBs have the potential to be innovative and life-enhancing. However, achieving this potential in practice depends on a range of other factors, including changes in the routine practices and organizational culture of adult social care services and ensuring users have access to appropriate documentation and support. Any conclusions drawn from the experiences of these early IB users must be treated with caution. The findings nevertheless indicate some of the issues that will need to be addressed as IBs are implemented more widely to replace conventional forms of adult social care provision

Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnold tongues open regions of multistability exist, and the parameter dependency of the dynamics becomes rather complex. This paper discusses the bifurcation structure inside the Arnold tongue with zero rotation number and includes a study of nonsmooth bifurcations that happen for large nonlinearity in the region with strange nonchaotic attractors.Comment: 25 pages, 22 colored figures in reduced quality, submitted to Int. J. of Bifurcation and Chaos, a supplementary website (http://www.mpipks-dresden.mpg.de/eprint/jwiersig/0004003/) is provide

Families of piecewise linear maps with constant Lyapunov exponent

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.Comment: 26 pages, 13 figure

Mechanisms of intermittent state transitions in a coupled heterogeneous oscillator model of epilepsy

This is the final version of the article. Available from BioMed Central/SpringerOpen via the DOI in this record.We investigate the dynamic mechanisms underlying intermittent state transitions in a recently proposed neural mass model of epilepsy. A low dimensional model is constructed, which preserves two key features of the neural mass model, namely (i) coupling between oscillators and (ii) heterogeneous proximity of these oscillators to a bifurcation between distinct limit cycles. We demonstrate that state transitions due to intermittency occur in the abstract model. This suggests that there is a general bifurcation mechanism responsible for this behaviour and that this is independent of the precise form of the evolution equations. Such abstractions of neural mass models allow a deeper insight into underlying dynamic and physiological mechanisms, and also allow the more efficient exploration of large scale brain dynamics in disease.MG acknowledges funding from the EPSRC through a postdoctoral prize fellowship

Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Simulating soil carbon sequestration from long term fertilizer and manure additions under continuous wheat using the DailyDayCent model

Bangabandhu Fellowship on Science and ICT project, Ministry of Science and Technology, People’s Republic of Bangladesh. Open Access via Springer Compact AgreementPeer reviewedPublisher PD

Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems

We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same network (polysynchronous states). These systems may have implications for the evolutionary emergence of polysynchrony and hierarchical networks in physical or biological systems modeled by adaptive networks.Comment: 4 pages, 4 figure