1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

http://people.physik.hu-berlin.de/~lindner/PDF/physreport.pdf

Effects of noise in excitable systems

Exploring and identifying structure is even more important for multivariate data than univariate data, given the difficulties in graphically presenting multivariate data and the comparative lack of parametric models to represent it. Unfortunately, such exploration is also inherently more difficult.

Multivariate Density Estimation

Nonlinear Oscillations: Exact Solutions and their Approximations

Reactive species in non-equilibrium atmospheric-pressure plasmas: Generation, transport, and biological effects

Cold atmospheric pressure helium plasma jets are increasingly used in many processing applications, due to a distinct combination of their inherent plasma stability with excellent reaction chemistry often enhanced downstream. Despite their widespread usage, it remains largely unknown whether cold atmospheric plasma jets maintain similar characteristics from breakdown to arcing or whether they possess different operating modes. In addition to their known ability to produce a fast moving train of discrete luminous clusters along the jet length, commonly known as plasma bullets, this paper reports evidence of two additional modes of operation, namely a chaotic mode and a continuous mode in an atmospheric helium plasma jet. Through detailed electrical and optical characterization, it is shown that immediately following breakdown the plasma jet operates in a deterministic chaotic mode. With increasing input power, the discharge becomes periodic and the jet plasma is found to produce at least one strong plasma bullet every cycle of the applied voltage. Further increase in input power eventually leads to the continuous mode in which excited species are seen to remain within the inter-electrode space throughout the entire cycle of the applied voltage. Transition from the chaotic, through the bullet, to the continuous modes is abrupt and distinct, with each mode having a unique set of operating characteristics. For the bullet mode, direct evidence is presented to demonstrate that the evolution of the plasma jet involves a repeated sequence of generation, collapse and regeneration of the plasma head occurring at locations progressively towards the instantaneous cathode. These offer previously unavailable insight into plasma jet formation mechanisms and the potential of matching plasma jet modes to specific needs of a given processing application.

/pdf/three-distinct-modes-in-a-cold-atmospheric-pressure-plasma-k1n7loqqv0.pdf

Three distinct modes in a cold atmospheric pressure plasma jet

General Mechanisms of Synchronization- General Remarks- 1?:?1 Forced Synchronization of Periodic Oscillations- 1?:?1 Mutual Synchronization of Periodic Oscillations- Homoclinic Mechanism of Synchronization of Periodic Oscillations- n?:?m Synchronization of Periodic Oscillations- 1?:?1 Forced Synchronization of Periodic Oscillations in the Presence of Noise- Chaos Synchronization- Synchronization of Noise-Induced Oscillations- Conclusions to Part I- Case Studies in Synchronization- Synchronization of Anisochronous Oscillators- Phase Multistability- Synchronization in Systems with Complex Multimode Dynamics- Synchronization of Systems with Resource Mediated Coupling- Conclusions to Part II

Synchronization: From Simple to Complex

Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the time scales of noise-induced motion by changing the time delay.

/pdf/delayed-feedback-as-a-means-of-control-of-noise-induced-4hut5cf0q1.pdf

Delayed Feedback as a Means of Control of Noise-Induced Motion

We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the R\"ossler system. We reveal the general bifurcation diagram in the parameter plane of time delay $\ensuremath{\tau}$ and feedback strength $K$ which allows one to explain the phenomena that have been discovered in some previous works. We show that the bifurcation diagram has essentially a multileaf structure that constitutes multistability: the larger the $\ensuremath{\tau}$, the larger the number of attractors that can coexist in the phase space. Feedback induces a large variety of regimes nonexistent in the original system, among them tori and chaotic attractors born from them. Finally, we estimate how the parameters of delayed feedback influence the periods of limit cycles in the system.

/pdf/delayed-feedback-control-of-chaos-bifurcation-analysis-3cmxhrgd4q.pdf

Delayed feedback control of chaos : Bifurcation analysis

We investigate feedback control of the cooperative dynamics of two coupled neural oscillators that is induced merely by external noise. The interacting neurons are modeled as FitzHugh-Nagumo systems with parameter values at which no autonomous oscillations occur, and each unit is forced by its own source of random fluctuations. Application of delayed feedback to only one of two subsystems is shown to be able to change coherence and time scales of noise-induced oscillations either in the given subsystem, or globally. It is also able to induce or to suppress stochastic synchronization under certain conditions.

Natalia B. Janson

Papers

Three distinct modes in a cold atmospheric pressure plasma jet

Synchronization: From Simple to Complex

Delayed Feedback as a Means of Control of Noise-Induced Motion

Delayed feedback control of chaos : Bifurcation analysis

Noise-induced cooperative dynamics and its control in coupled neuron models.