# Browsing by Author "Rachinskii, Dmitry I."

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Item Analytical Solution for a Class of Network Dynamics with Mechanical and Financial Applications(Published By The American Physical Society Through The American Institute Of Physics, 2014-09-29) Krej?©, P.; Lamba, H.; Melnik, S.; Rachinskii, Dmitry I.; 0000 0003 5341 0057 (Rachinskii, DI); Rachinskii, Dmitry I.Show more We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.Show more Item Bistability and Hysteresis in an Optically Injected Two-Section Semiconductor Laser(Amer Physical Soc, 2014-05-08) Pimenov, A.; Viktorov, E. A.; Hegarty, S. P.; Habruseva, T.; Huyet, G.; Rachinskii, Dmitry I.; Vladimirov, A. G.; 0000 0003 5341 0057 (Rachinskii, DI); Rachinskii, Dmitry I.Show more The effect of coherent single frequency injection on two-section semiconductor lasers is studied numerically using a model based on a set of delay differential equations. The existence of bistability between different continuous-wave and nonstationary regimes of operation is demonstrated in the case of sufficiently large linewidth enhancement factors.Show more Item Chaos In Saw Map(World Scientific Publ Co Pte Ltd, 2019-02) Begun, Nikita; Kravetc, Pavel; Rachinskiy Dmitry I.; Rachinskii, Dmitry I.Show more We consider the dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincare map of simple two-dimensional discrete time piecewise linear systems involving a saturation function. Alternatively, these systems can be viewed as a feedback loop with the so-called stop hysteresis operator. We analyze chaotic sets and attractors of the "saw map" depending on its parameters.Show more Item Effect of Dynamical Instability on Timing Jitter in Passively Mode-Locked Quantum-Dot Lasers(Optical Soc Amer, 2014-12-08) Pimenov, A.; Habruseva, T.; Rachinskii, Dmitry I.; Hegarty, S. P.; Huyet, G.; Vladimirov, A. G.; 0000 0003 5341 0057 (Rachinskii, DI); Rachinskii, Dmitry I.Show more We study the effect of noise on the dynamics of passively mode-locked semiconductor lasers both experimentally and theoretically. A method combining analytical and numerical approaches for estimation of pulse timing jitter is proposed. We investigate how the presence of dynamical features such as wavelength bistability in a quantum-dot laser affects timing jitter.Show more Item Hysteresis Can Grant Fitness in Stochastically Varying Environment(Public Library of Science, 2014-07-28) Friedman, Gary; McCarthy, Stephen; Rachinskii, Dmitry I.; 0000 0003 5341 0057 (Rachinskii, DI); Rachinskii, Dmitry I.Show more Although the existence of multiple stable phenotypes of living organisms enables random switching between phenotypes as well as non-random history dependent switching called hysteresis, only random switching has been considered in prior experimental and theoretical models of adaptation to variable environments. This work considers the possibility that hysteresis may also evolve together with random phenotype switching to maximize population growth. In addition to allowing the possibility that switching rates between different phenotypes may depend not only on a continuous environmental input variable, but also on the phenotype itself, the present work considers an opportunity cost of the switching events. This opportunity cost arises as a result of a lag phase experimentally observed after phenotype switching and stochastic behavior of the environmental input. It is shown that stochastic environmental variation results in maximal asymptotic growth rate when organisms display hysteresis for sufficiently slowly varying environmental input. At the same time, sinusoidal input does not cause evolution of memory suggesting that the connection between the lag phase, stochastic environmental variation and evolution of hysteresis is a result of a stochastic resonance type phenomenon.Show more Item Periodic Canard Trajectories with Multiple Segments Following the Unstable Part of Critical Manifold(2012-11-01) Krasnosel'skii, Alexander M.; O'Grady, Edward; Pokrovskii, Alexei V.; Rachinskii, Dmitry I.; 0000 0003 5341 0057 (Rachinskii, DI); Rachinskii, Dmitry I.Show more We consider a scalar fast differential equation which is periodically driven by a slowly varying input. Assuming that the equation depends on n scalar parameters, we present simple sufficient conditions for the existence of a periodic canard solution, which, within a period, makes n fast transitions between the stable branch and the unstable branch of the folded critical curve. The closed trace of the canard solution on the plane of the slow input variable and the fast phase variable has n portions elongated along the unstable branch of the critical curve. We show that the length of these portions and the length of the time intervals of the slow motion separated by the short time intervals of fast transitions between the branches are controlled by the parameters.Show more Item Periodic Pulsating Dynamics of Slow-Fast Delayed Systems with a Period Close to the Delay(Cambridge Univ Press, 2017-12-22) Kravetc, Pavel; Rachinskii, Dmitry I.; Vladimirov, A.; Kravetc, Pavel; Rachinskii, Dmitry I.Show more We consider slow-fast delayed systems and discuss pulsating periodic solutions, which are characterised by specific properties that (a) the period of the periodic solution is close to the delay, and (b) these solutions are formed close to a bifurcation threshold. Such solutions were previously found in models of mode-locked lasers. Through a case study of population models, this work demonstrates the existence of similar solutions for a rather wide class of delayed systems. The periodic dynamics originates from the Hopf bifurcation on the positive equilibrium. We show that the continuous transformation of the periodic orbit to the pulsating regime is simultaneous with multiple secondary almost resonant Hopf bifurcations, which the equilibrium undergoes over a short interval of parameter values. We derive asymptotic approximations for the pulsating periodic solution and consider scaling of the solution and its period with the small parameter that measures the ratio of the time scales. The role of competition for the realisation of the bifurcation scenario is highlighted.Show more