Classification of coupled dynamical systems with multiple delays: Finding the minimal number of delays

In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We prove that for particular sets of delays this is not the case. To this aim we introduce a componentwise timeshift transformation (CTT) which allows to classify systems which possess equivalent dynamics, though possibly different sets of connection delays. In particular, we show for a large class of semiflows (including the case of delay differential equations) that the stability of attractors is invariant under this transformation. Moreover we show that each equivalence class which is mediated by the CTT possesses a representative system in which the number of different delays is not larger than the cycle space dimension of the underlying graph. We conclude that the 'true' dimension of the corresponding parameter space of delays is in general smaller than it appears at first glance

Detection and storage of multivariate temporal sequences by spiking pattern reverberators

We consider networks of spiking coincidence detectors in continuous time. A single detector is a finite state machine that emits a pulsatile signal whenever the number incoming inputs exceeds a threshold within a time window of some tolerance width. Such finite state models are well-suited for hardware implementations of neural networks, as on integrated circuits (IC) or field programmable arrays (FPGAs) but they also reflect the natural capability of many neurons to act as coincidence detectors. We pay special attention to a recurrent coupling structure, where the delays are tuned to a specific pattern. Applying this pattern as an external input leads to a self-sustained reverberation of the encoded pattern if the tuning is chosen correctly. In terms of the coupling structure, the tolerance and the refractory time of the individual coincidence detectors, we determine conditions for the uniqueness of the sustained activity, i.e., for the funcionality of the network as an unambiguous pattern detector. We also present numerical experiments, where the functionality of the proposed pattern detector is demonstrated replacing the simplistic finite state models by more realistic Hodgkin-Huxley neurons and we consider the possibility of implementing several pattern detectors using a set of shared coincidence detectors. We propose that inhibitory connections may aid to increase the precision of the pattern discrimination

Multistable jittering in oscillators with pulsatile delayed feedback

Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a periodic regular spiking regime. In the bifurcation point numerous regimes with non-equal interspike intervals emerge simultaneously. We show that this bifurcation is triggered by the steepness of the oscillator's phase resetting curve and that the number of the emerging, so-called "jittering" regimes grows exponentially with the delay value. Although this appears as highly degenerate from a dynamical systems viewpoint, the "multi-jitter" bifurcation occurs robustly in a large class of systems. We observe it not only in a paradigmatic phase-reduced model, but also in a simulated Hodgkin-Huxley neuron model and in an experiment with an electronic circuit

Spectrum and amplitude equations for scalar delay-differential equations with large delay

The subject of the paper are scalar delay-differential equations with large delay. Firstly, we describe the asymptotic properties of the spectrum of linear equations. Using these properties, we classify possible types of destabilization of steady states. In the limit of large delay, this classification is similar to the one for parabolic partial differential equations. We present a derivation and error estimates for amplitude equations, which describe universally the local behavior of scalar delay-differential equations close to the destabilization threshold

Noise enhanced coupling between two oscillators with long-term plasticity

Spike time-dependent plasticity is a fundamental adaptation mechanism of the nervous system. It induces structural changes of synaptic connectivity by regulation of coupling strengths between individual cells depending on their spiking behavior. As a biophysical process its functioning is constantly subjected to natural fluctuations. We study theoretically the influence of noise on a microscopic level by considering only two coupled neurons. Adopting a phase description for the neurons we derive a two-dimensional system which describes the averaged dynamics of the coupling strengths. We show that a multistability of several coupling configurations is possible, where some configurations are not found in systems without noise. Intriguingly, it is possible that a strong bidirectional coupling, which is not present in the noise-free situation, can be stabilized by the noise. This means that increased noise, which is normally expected to desynchronize the neurons, can be the reason for an antagonistic response of the system, which organizes itself into a state of stronger coupling and counteracts the impact of noise. This mechanism, as well as a high potential for multistability, is also demonstrated numerically for a coupled pair of Hodgkin-Huxley neurons

Reinforcement Learning-based Traffic Control: Mitigating the Adverse Impacts of Control Transitions

An important aspect of automated driving is to handle situations where it fails or is not allowed in specific traffic situations. This case study explores means, by which control transitions in a mixed autonomy system can be organized in order to minimize their adverse impact on traffic flow. We assess a number of different approaches for a coordinated management of transitions, covering classic traffic management paradigms and AI-driven controls. We demonstrate that they yield excellent results when compared to a do-nothing scenario. This text further details a model for control transitions that is the basis for the simulation study presented. The results encourage the deployment of reinforcement learning on the control problem for a scenario with mandatory take-over requests

Two-cluster bifurcations in systems of globally pulse-coupled oscillators

For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via bifurcations. The coupling is modeled using the phase-response-curve (PRC), which measures the sensitivity of each oscillator's phase to perturbations. For large systems with a PRC, which turns to zero at the spiking threshold, we are able to find the parameter regions where multiple stable two-cluster states coexist and illustrate this by an example. In addition, we explain how a locally unstable one-cluster state may form an attractor together will its homoclinic connections. This leads to the phenomenon of intermittent, asymptotic synchronization with abating beats away from the perfect synchrony.Comment: 12 pages. 6 figure

MAVEN Deliverable 7.2: Impact Assessment - Technical Report

This deliverable focuses on an important topic within the MAVEN project - evaluation of the project impact. This is an important step that will allow us to say what the results and impact of the different technologies, functionalities as well as assumptions are. It covers different dimensions of the impact assessment as stated in the Deliverable D7.1 - Impact assessment plan [10]. The field tests proved that the technology in the vehicle works together with the infrastructure and the solution is technically feasible. This was demonstrated also during particular events and is reported in the attached test protocols. At the same time, the emulation and simulation in Dominion software proved the functionality, for example with respect to the cooperative perception or safety indicators. The tests also proved that the key performance indicator "minimum time to the collision" decreases when applying the cooperative sensing. Also, the number of human interventions needed was zero in all the tests. This deliverable also discussed selected results of a detailed user survey aiming at understanding the expected impacts and transition of automated vehicles. The overall number of respondents reached 209. The responses have revealed some interesting facts. For example, over 80% of the respondents believe that CAVs will decrease the number of traffic accidents. Similarly, about 70% of the respondents expect improvements in traffic congestions. Over 82% of respondents declared that they would accept some detour when driving if it helps the overall traffic situation. The literature review, however, indicated that autonomous vehicles will have either a positive or a negative effect on the environment, depending on the policies. For example, opening cars as a mode of transport to new user groups (seniors, children etc.) together with improvements of the traffic, flow parameters can increase the traffic volume on roads. Policy makers shall focus on the integration of the CAVs into a broader policy concept including car or ride-sharing, electromobility and others. In order to evaluate the transition, for example, the influence of different penetration rates of CAVs on the performance, a microscopic traffic simulation was performed. Here the particular MAVEN use cases, as well as their combination, was addressed. The results of the simulation are rather promising. The potential for improvements in traffic performance is clearly there. It was demonstrated that a proper integration of CAVs into city traffic management can, for example, help with respect to the environmental goals (Climate Action of the European Commission) and reduce CO2 emissions by up to 12 % (a combination of GLOSA and signal optimization). On corridors with a green wave, a capacity increase of up to 34% was achieved. The conclusions from this project can be used not only by other researchers but mainly by traffic managers and decision-makers in cities. The findings can get a better idea about the real impacts of particular use cases (such as green wave, GLOSA and others) in the cities. An important added value is also the focus on the transition phase. It was demonstrated that already for lower penetration rates (even 20% penetration of automated vehicles), there are significant improvements in traffic performance. For example, the platooning leads to a decrease of CO2 emissions of 2,6% or the impact indicator by 17,7%

TransAID Deliverable 6.2/2 - Assessment of Traffic Management Procedures in Transition Areas

This Deliverable 6.2 of the TransAID project presents and evaluates the simulation results obtained for the scenarios considered during the project's first and second iterations. To this end, driver- and AV-models designed in WP3, traffic management procedures developed in WP4, and V2X communication protocols and models from WP5 were implemented within the iTETRIS simulation framework. Previous main results from Deliverable 4.2, where baseline and traffic management measures without V2X communication were compared, have been confirmed. While not all TransAID scenarios' traffic KPIs were affected, the realistic simulation of V2X communication has shown a discernible impact on some of them, which makes it an indispensable modelling aspect for a realistic performance evaluation of V2X traffic scenarios. Flaws of the first iteration's traffic management algorithms concerning wireless V2X communication and the accompanying possibility of packet loss were identified and have been addressed during the project's second iteration. Finally, lessons learned while working on these simulation results and assessments have additionally been described in the form of recommendations for the real-world prototype to be developed in WP7. We conclude that all results obtained for all scenarios when employing ideal communication confirmed the statistical trends of the results from the original TM scenarios as reported in Deliverable 4.2 where no V2X communication was considered. Furthermore, the performance evaluation of the considered scenarios and parameter combinations has shown the following, which held true in both the first and second iterations: (1) The realistic simulation of V2X communication has an impact on traffic scenarios, which makes them indispensable for a realistic performance evaluation of V2X traffic scenarios. (2) Traffic management algorithms need to account for sporadic packet loss of various message types in some way. (3) Although important, the realistic modelling and simulation of V2X communication also induces a significant computational overhead. Thus, from a general perspective, a trade-off between computation time and degree of realism should be considered