Browsing by Author "Atay, F. M."
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Item Open Access Characterization of exact lumpability for vector fields on smooth manifolds(Elsevier, 2016) Horstmeyer, L.; Atay, F. M.We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various results from the literature that exist for Euclidean spaces. We introduce a partial connection on the pullback bundle that is related to the Bott connection and behaves like a Lie derivative. The lumping conditions are formulated in terms of the differential of the lumping map, its covariant derivative with respect to the connection and their respective kernels. Some examples are discussed to illustrate the theory. © 2016 Published by Elsevier B.V.Item Open Access Local pinning of networks of multi-agent systems with transmission and pinning delays(Institute of Electrical and Electronics Engineers, 2016) Lu, W.; Atay, F. M.We study the stability of networks of multi-agent systems with local pinning strategies and two types of time delays, namely the transmission delay in the network and the pinning delay of the controllers. Sufficient conditions for stability are derived under specific scenarios by computing or estimating the dominant eigenvalue of the characteristic equation. In addition, controlling the network by pinning a single node is studied. Moreover, perturbation methods are employed to derive conditions in the limit of small and large pinning strengths. Numerical algorithms are proposed to verify stability, and simulation examples are presented to confirm the efficiency of analytic results. � 2015 IEEE.Item Open Access Lumpability of linear evolution equations in banach spaces(American Institute of Mathematical Sciences, 2017) Atay, F. M.; Roncoroni, L.We analyze the lumpability of linear systems on Banach spaces, namely, the possibility of projecting the dynamics by a linear reduction opera-tor onto a smaller state space in which a self-contained dynamical description exists. We obtain conditions for lumpability of dynamics defined by unbounded operators using the theory of strongly continuous semigroups. We also derive results from the dual space point of view using sun dual theory. Furthermore, we connect the theory of lumping to several results from operator factoriza-tion. We indicate several applications to particular systems, including delay differential equations. © 2017, American Institute of Mathematical Sciences. All rights reserved.Item Open Access On the Delay Margin for Consensus in Directed Networks of Anticipatory Agents(Elsevier B.V., 2016) Irofti D.; Atay, F. M.We consider a linear consensus problem involving a time delay that arises from predicting the future states of agents based on their past history. In case the agents are coupled in a connected and undirected network, the exact condition for consensus is that the delay be less than a constant threshold that is independent of the network topology or size. In directed networks, however, the situation is quite different. We show that the allowable maximum delay for consensus depends on the network topology in a nontrivial way. We study this delay margin in several network constellations, including various circulant networks with directed links. We show that the delay margin depends not only on the number of neighbors, but also on the directionality of connections with those neighbors. Furthermore, the delay margin improves as the circulant networks are rewired en route to a small-world configuration. © 2016Item Open Access Stability regions for synchronized τ-periodic orbits of coupled maps with coupling delay τ(American Institute of Physics, 2016) Karabacak, Ö.; Alikoç, B.; Atay, F. M.Motivated by the chaos suppression methods based on stabilizing an unstable periodic orbit, westudy the stability of synchronized periodic orbits of coupled map systems when the period of theorbit is the same as the delay in the information transmission between coupled units. We show thatthe stability region of a synchronized periodic orbit is determined by the Floquet multiplier of theperiodic orbit for the uncoupled map, the coupling constant, the smallest and the largest Laplacianeigenvalue of the adjacency matrix. We prove that the stabilization of an unstable τ-periodic orbitvia coupling with delay τ is possible only when the Floquet multiplier of the orbit is negative andthe connection structure is not bipartite. For a given coupling structure, it is possible to find thevalues of the coupling strength that stabilizes unstable periodic orbits. The most suitableconnection topology for stabilization is found to be the all-to-all coupling. On the other hand, anegative coupling constant may lead to destabilization of τ-periodic orbits that are stable for theuncoupled map. We provide examples of coupled logistic maps demonstrating the stabilization anddestabilization of synchronized τ-periodic orbits as well as chaos suppression via stabilization of asynchronized τ-periodic orbit.