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Coherent terahertz (THz) radiations based on intrinsic Josephson junctions (IJJs) from a Bi2Sr2CaCu2O[Formula: see text] (BSCCO) mesa under a bias voltage were observed in 2007. Later on, a novel [Formula: see text] phase kink state was proposed which can explain the key experimental results. However, how to drive the system into the [Formula: see text] phase kink state efficiently still remains an open problem. In this work, we propose several ways to synchronize the system to the [Formula: see text] phase kink state. We start from random and typical regular initial phase configurations. It is found that starting from some initial phase configurations, the system can be driven efficiently into the [Formula: see text] phase kink state. The time spent before entering the [Formula: see text] phase kink states for these initial phase configurations is shorter when the initial phase configuration is further away from the uniform phase configuration.

The individual functional unit of the kidney (the nephron) displays oscillations in its pressure and flow regulation at two different time scales: Relatively fast oscillations associated with the myogenic dynamics of the afferent arteriole, and slower oscillations related with a delay in the tubuloglomerular feedback. Neighboring nephrons interact via vascularly propagated signals. We study the appearance of various forms of coherent behavior in a model of two such interacting nephrons. Among the observed phenomena are in-phase and anti-phase synchronization of chaotic dynamics, multistability, and partial phase synchronization in which the nephrons attain a state of chaotic phase synchronization with respect to their slow dynamics, but the fast dynamics remains desynchronized.

Phase synchronization of parametric excited Rössler system has been investigated in this paper. By introducing the conception of phase for a chaotic motion, it has been demonstrated that the mean frequency of chaotic attractor and the frequency of the parametric excitation may be locked in different ratios for certain parameter conditions, implying phase synchronization can be observed. The evolution from nonsynchronized state to phase synchronization has been discussed in detail, which reveals different phase dynamics may exist during the process. With the variation of parameters, the imaging point on the Poincaré plane may finally settle down onto the attractor, which yields phase synchronization.

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, we tune the linear coupling parameter to obtain the two Rössler oscillators in a synchronized regime and analyze the effect of a nonlinear coupling on the phase synchronized state. It demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase of the nonlinear coupling strength, for the primary resonance, the effect of phase synchronization between two sub-systems was decayed, while increasing with frequency ratio 1:2. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the nonlinear coupling strength.

The dynamical responses of an excitable FitzHugh–Nagumo (FHN) system under the drive of an external noise are studied. Noise can induce a sequence of firings. The n:m coherent resonance of the FHN oscillator with an intrinsic natural frequency is shown. This effect is discussed by resorting to the phase dynamics of a spike train and the phase synchronization index γnm.

We study effects of noise in two types of chaotic oscillators. The first one, represented by the Rössler system, has very coherent phase dynamics while the amplitude fluctuates strongly. The other type, homoclinic chaos characterized by chaotic spiking behavior, has regular orbits in the phase space while the interspike time intervals vary enormously. We demonstrate that in both classes of systems, noise may play a constructive role to enhance synchronization and generate the most coherent behavior in the collective oscillation of coupled phase coherent oscillators or in the spike sequences of homoclinic chaos.

We propose a theoretical model to account for the increase in the effect of both magnetic induction and presence of a nonequilibrium state in layered superconductors which behave as intrinsic Josephson junctions. Using this model, we investigate the phase dynamics with a magnetic field applied parallel to the superconducting layers and show that the increase in the coupling between the superconducting layers due to the increase in the effect of magnetic induction and the departure from equilibrium significantly modifies the dispersion of the Josephson plasma mode in intrinsic Josephson junctions from that in conventional stacks of Josephson junctions.

We investigate the Hubbard Hamiltonian's properties in the continuum limit by implementing the procedures of the Method of Coherent Structures (MCS). We obtain field equations of motion and analyse the phase dynamics of the resultant classical spin fields. We have performed analytical and numerical calculations to find appropriate physically acceptable solutions to the equations of motion in one-dimensional space. In two-dimensional space, among other types, we have found several different spin phases of vortex type, spiral patterns and parabolic spin arrangements. Our results are consistent with earlier Hartree–Fock finite-grid numerical simulations.