Anomalous behavior of synchronization in a mutually coupled identical thomas oscillators

Synchronization in a mutually coupled identical Thomas oscillators with non-linear coupling schemes show unusual characteristics than with linear coupling. Linearly coupled systems show expected complete synchronization (CS). Whereas with non-linear coupling there are windows of lag(LS) or anti-lag(ALS) synchronizations after CS in the intermediate rage of coupling followed by CS again, not achieved earlier. More new features in synchronization are observed for a small window of both types of coupling when uncoupled system's dynamics is at the border of chaotic and quasi-periodic regimes. The stability of synchronized states in all the cases for weak and moderate coupling remain slightly below the stable-unstable boundary towards the stable region. Therefore stable synchronized states are not too sensitive to perturbation, means perturbation dies very slowly.Comment: 16 pages, 21 figure

Stability of the nonlinear dynamics of an optically injected VCSEL

Automated protocols have been developed to characterize time series data in terms of stability. These techniques are applied to the output power time series of an optically injected vertical cavity surface emitting laser (VCSEL) subject to varying injection strength and optical frequency detuning between master and slave lasers. Dynamic maps, generated from high resolution, computer controlled experiments, identify regions of dynamic instability in the parameter space. © 2012 Optical Society of America

Rössler-network with time delay : Univariate impulse pinning synchronization

ACKNOWLEDGMENTS: This paper was supported in part by the Shaanxi Provincial Special Support Program for Science and Technology Innovation Leader.Peer reviewedPostprintPublisher PD

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA