Phase synchronization of chaos is studied using a modified Rössler system. By employing a lift of the phase variable (i.e., phase points separated by 2p are not considered as the same), the transition to phase synchronization is viewed as a boundary crisis mediated by an unstable-unstable pair bifurcation on a branched manifold, and the accompanying basin boundary structure is found to be of a new type.[S0031-9007(98)05362-9] PACS numbers: 05.45. + b, 02.40.Sf

Experimental phase synchronization of chaos in a plasma discharge is studied using a phase variable lift technique (i.e., phase points separated by 2pi are not considered as the same). Real-time observation of synchronized and unsynchronized states is made possible through a real-time sampling procedure. Parameter space regions of synchronization and unsynchronization are identified, and a set of equations is suggested to model the real plasma circuit.

Long-range communication in the nervous system is usually carried out with the propagation of action potentials along the axon of nerve cells. While typically thought of as being unidirectional, it is not uncommon for axonal propagation of action potentials to happen in both directions. This is the case because action potentials can be initiated at multiple "ectopic" positions along the axon. Two ectopic action potentials generated at distinct sites, and traveling toward each other, will collide. As neuronal information is encoded in the frequency of action potentials, action potential collision and annihilation may affect the way in which neuronal information is received, processed, and transmitted. We investigate action potential propagation and collision using an axonal multicompartment model based on the Hodgkin-Huxley equations. We characterize propagation speed, refractory period, excitability, and action potential collision for slow (type I) and fast (type II) axons. In addition, our studies include experimental measurements of action potential propagation in axons of two biological systems. Both computational and experimental results unequivocally indicate that colliding action potentials do not pass each other; they are reciprocally annihilated.

Experimental phase synchronization of chaos is demonstrated for a plasma discharge tube subject to a high dc voltage (800-900 V), and paced with a low amplitude (less than 1 V) wave generator.

We show experimental and numerical results of phase synchronization between the chaotic Chua circuit and a small sinusoidal perturbation. Experimental real-time phase synchronized states can be detected with oscilloscope visualization of the attractor, using specific sampling rates. Arnold tongues demonstrate robust phase synchronized states for perturbation frequencies close to the characteristic frequency of the unperturbed Chua.

Despite efforts to integrate research across different subdisciplines of biology, the scale of integration remains limited. We hypothesize that future generations of Artificial Intelligence (AI) technologies specifically adapted for biological sciences will help enable the reintegration of biology. AI technologies will allow us not only to collect, connect and analyze data at unprecedented scales, but also to build comprehensive predictive models that span various subdisciplines. They will make possible both targeted (testing specific hypotheses) and untargeted discoveries. AI for biology will be the cross-cutting technology that will enhance our ability to do biological research at every scale. We expect AI to revolutionize biology in the 21st century much like statistics transformed biology in the 20th century. The difficulties, however, are many, including data curation and assembly, development of new science in the form of theories that connect the subdisciplines, and new predictive and interpretable AI models that are more suited to biology than existing machine learning and AI techniques. Development efforts will require strong collaborations between biological and computational scientists. This white paper provides a vision for AI for Biology and highlights some challenges.

We present a novel modeling approach for reconstruction of the global behavior of coupled chaotic systems from bivariate time series. We analyze two coupled chaotic oscillators, which are able to phase synchronize due to coupling. It is shown that our technique enables the recovery of the synchronization diagram from only three data sets. In particular, this allows the estimate of the relative strength of the coupling and the parameter mismatch of both subsystems. The method is most efficient if only data from the nonsynchronized regime are used for the model learning. We also apply this approach to experimental data of a paced plasma tube.

We present the characteristics and an analysis of a proposed communication scheme fully based on chaos theory. The key point is that the proposed scheme introduces the dynamical system as a way to encode and decode information and as a signal wave generator. In this scheme, all the protocols used to communicate digitally are fully integrated into one single design based on a chaotic modulation process. The chaotic encoder finds a set of trajectories that codes the information into a hard to decode chaotic wave form that carries a large amount of information. We also show how our scheme can handle multiplexing, which is also used as a way to enhance security, and its ability to handle noise.