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 characterisation, 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.

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.

We propose a method to control noise-induced motion, based on using delayed feedback in the form of the difference between the delayed and the current states of the system. The method is applied to two different types of systems, namely, a selfoscillator near Andronov-Hopf bifurcation and a threshold system. In both cases we demonstrate that by variation of time delay one can effectively control coherence and timescales of stochastic oscillations. The entrainment of the basic period of oscillations by time delay is discovered. We give explanations of the phenomena observed and provide a theory for the system near bifurcation.

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.

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We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the Rössler system. We reveal the general bifurcation diagram in the parameter plane of time delay τ 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 multi-leaf structure that constitutes multistability: the larger the τ , the larger the number of attractors that can coexist in the phase space. Feedback induces a large variety of regimes non-existent 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.

We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of the control force. Approximate analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation are developed, and are in good agreement with our numerical simulations. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay and feedback strength.