Challenges in Complex Systems Science

FuturICT foundations are social science, complex systems science, and ICT. The main concerns and challenges in the science of complex systems in the context of FuturICT are laid out in this paper with special emphasis on the Complex Systems route to Social Sciences. This include complex systems having: many heterogeneous interacting parts; multiple scales; complicated transition laws; unexpected or unpredicted emergence; sensitive dependence on initial conditions; path-dependent dynamics; networked hierarchical connectivities; interaction of autonomous agents; self-organisation; non-equilibrium dynamics; combinatorial explosion; adaptivity to changing environments; co-evolving subsystems; ill-defined boundaries; and multilevel dynamics. In this context, science is seen as the process of abstracting the dynamics of systems from data. This presents many challenges including: data gathering by large-scale experiment, participatory sensing and social computation, managing huge distributed dynamic and heterogeneous databases; moving from data to dynamical models, going beyond correlations to cause-effect relationships, understanding the relationship between simple and comprehensive models with appropriate choices of variables, ensemble modeling and data assimilation, modeling systems of systems of systems with many levels between micro and macro; and formulating new approaches to prediction, forecasting, and risk, especially in systems that can reflect on and change their behaviour in response to predictions, and systems whose apparently predictable behaviour is disrupted by apparently unpredictable rare or extreme events. These challenges are part of the FuturICT agenda

Birth and Death of Chimera: Interplay of Delay and Multiplexing

The chimera state with co-existing coherent-incoherent dynamics has recently attracted a lot of attention due to its wide applicability. We investigate non-locally coupled identical chaotic maps with delayed interactions in the multiplex network framework and find that an interplay of delay and multiplexing brings about an enhanced or suppressed appearance of chimera state depending on the distribution as well as the parity of delay values in the layers. Additionally, we report a layer chimera state with an existence of one layer displaying coherent and another layer demonstrating incoherent dynamical evolution. The rich variety of dynamical behavior demonstrated here can be used to gain further insight into the real-world networks which inherently possess such multi-layer architecture with delayed interactions

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator reaches a specific state, it emits a pulse, which returns after propagating through a delay line. The impact of an incoming pulse is described by the oscillator's phase reset curve (PRC). In such a system we discover an unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value. The number of such critical multipliers increases linearly with the delay and thus may be arbitrary large. This bifurcation is accompanied by the emergence of numerous "jittering" regimes with non-equal interspike intervals (ISIs). Each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay. The number of different "jittering" solutions emerging at the bifurcation point increases exponentially with the delay. We describe the combinatorial mechanism that underlies the emergence of such a variety of solutions. In particular, we show how a periodic solution exhibiting several distinct ISIs can imply the existence of multiple other solutions obtained by rearranging of these ISIs. We show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback

Evolutionary robotics and neuroscience

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Controllability of Cardiac Alternans

An arrhythmia is a disorder in the heart that occurs due to irregular or abnormal heartbeats. There are many types of arrhythmias, some of which are harmless, but some, including ventricular tachycardia and fibrillation, can be life-threatening. Certain arrhythmias are preceded by electrical alternans, which is a state characterized by beat-to-beat alternation in cellular action potential duration. Cardiac alternans may arise from instabilities in either voltage or intracellular calcium cycling. Although a number of techniques have been proposed to suppress alternans, most have focused on appropriately adding a new ionic current or adjusting the timing of pacing stimuli based on the difference between recent action potential durations, rather than affecting intracellular calcium directly. In addition, most of the methods proposed to suppress alternans have been tested using models that do not include calcium-driven alternans. Therefore, it is important to establish a theoretical basis for understanding how control methods may apply when alternans is driven by instabilities in calcium cycling. In this study, we apply controllability analysis to a discrete map of alternans dynamics in a cardiac cell. In particular, we compare three different controllability measures to determine to what extent different control strategies can suppress alternans. The modal controllability measure was found to be the most informative measure, with effective variables through which to apply control being action potential duration regardless of alternans mechanism along with sarcoplasmic reticulum calcium load in the calcium-driven alternans case. Moreover, we designed and compared three feedback controllers, with the aim of suppressing alternans, based on our controllability results. As expected, full state feedback methods, such as pole placement and the Linear Quadratic Regulator, were more successful in stabilizing unstable alternans modes compared with feedback based on a single variable. We also conducted preliminary work on analyzing controllability of a different model of cardiac alternans described by nonlinear differential equations. Our study provides insight into the feasibility of controlling alternans driven wholly or partially by voltage or intracellular calcium instabilities