Delay-induced self-oscillation excitation in the FitzHugh-Nagumo model: regular and chaotic dynamics

The stochastic FitzHugh-Nagumo model with time delayed-feedback is often studied in excitable regime to demonstrate the time-delayed control of coherence resonance. Here, we show that the impact of time-delayed feedback in the FitzHugh-Nagumo neuron is not limited by control of noise-induced oscillation regularity (coherence), but also results in excitation of the regular and chaotic self-oscillatory dynamics in the deterministic model. We demonstrate this numerically by means of simulations, linear stability analysis, the study of Lyapunov exponents and basins of attraction for both positive and negative delayed-feedback strengths. It has been established that one can implement a route to chaos in the explored model, where the intrinsic peculiarities of the Feigenbaum scenario are exhibited. For large time delay, we complement the study of temporal evolution by the interpretation of the dynamics as patterns in virtual space.Comment: 12 pages, 11 figures in the main text and 3 figures in appendi

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To relax the local authorities and to receive the guests of high rank «with no tie» the so-called «Fisherman's House» was built at the source of Angara-river, near Lake Baikal. Vladimir Ivanov, a young architect, was noticed by his skillful performa nee of exclusive orders and became the author of this house. At the time of ferroconcrete boom the proposal to build a wooden guest house turned out to be unexpectedly to the point and was graciously approved. The economic department was entrusted to select the men good for carpenter's work, and the forestry department was entrusted to provide thick round timber. And the work started. But, as it usually happens, the workers did not take the trouble and made the first eight rims of the current timber with an inappropriate diameter.And when Pavlov insisted on demolishing the construction and replacing the logs by the logs with the necessary diameter, the building work obeyed to his will and was finished suecessfully.The architecture of the house is not the derived action of the saw and the fret-saw. It is a technology of the axe. It is natural, convincing and original. It is no use to look for the local sources in it. It grew up in the area of timber and cold winter. And this clear and efficient action kept the construction from the annoying vulgarity and provided Siberian exotics easily penetrating into one's soul, refined as it may be.One of the eminent guests said with admiration: «Even if Pavlov had created nothing more, he would have justified his professional choice with this single house.» Why not to say it as a good toast. However, this is a suitable case to add: style is an absence of style. It is a taste.After the Fisherman's House Irkutsk architects were attracted by wood. They followed the strictness in wood and, as much as they could, created a couple of successful remakes, until the cylinder logs and ... new Russian architects appeared. With their own aesthetics.After Pavlov had left Irkutsk, near his house appeared another one, it was not a log house, and its style was glaringly unfriendly. And soon the Fisherman's House burnt down. Not with vexation, but naturally, with smoke and fire. The author of the building next door considers the rebuilding of the lost house unpractical

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For the topic of this issue we have chosen the environment's component that remains after the grand architecture – the ground between buildings and smaller forms that fill it. It is painful that this subject turns out to be of little significance for our urbanists. The residual principle of treatment of land reclamation culture imparts disorder, hasty temporariness to our cities, as if we are not residents here. The topic's urgency has to be proven by other's experience