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Analytical approach for the Floquet theory of delay differential equations.
We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determiningExpand
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Analytical and numerical investigations of the phase-locked loop with time delay.
  • M. Schanz, A. Pelster
  • Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and…
  • 14 May 2003
We derive the normal form for the delay-induced Hopf bifurcation in the first-order phase-locked loop with time delay by the multiple scaling method. The resulting periodic orbit is confirmed byExpand
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Variational calculation of the limit cycle and its frequency in a two-neuron model with delay.
We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delayExpand
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Fluctuating paths and fields : festschrift dedicated to Hagen Kleinert on the occasion of his 60th birthday
Part 1 Path integrals and quantum mechanics: semiclassical quantum mechanics - a path-integral approach, B.R. Holstein conjecture on the reality of spectra of non-Hermetian Hamiltonians, C.M. BenderExpand
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Selforganization in Complex Systems: The Past, Present, and Future of Synergetics
Prices in financial markets exhibit extreme jumps far more often than can be accounted for by external news. Further, magnitudes of price changes are correlated over long times. These so calledExpand
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High-order variational calculation for the frequency of time-periodic solutions.
We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to theExpand
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Measuring finite-range phase coherence in an optical lattice using Talbot interferometry
One of the important goals of present research is to control and manipulate coherence in a broad variety of systems, such as semiconductor spintronics, biological photosynthetic systems,Expand
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Synergetic System Analysis for the Delay-Induced Hopf Bifurcation in the Wright Equation
We apply the synergetic elimination procedure for the stable modes in nonlinear delay systems close to a dynamical instability and derive the normal form for the delay-induced Hopf bifurcation in theExpand
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Synchronization in a neuronal feedback loop through asymmetric temporal delays
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when theExpand
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Excitation spectra of bosons in optical lattices from the Schwinger-Keldysh calculation
Within the Schwinger-Keldysh formalism we derive a Ginzburg-Landau theory for the Bose-Hubbard model which describes the real-time dynamics of the complex order parameter field. Analyzing theExpand
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