Synchronization of the Frenet-Serret linear system with a chaotic nonlinear system by feedback of states

A synchronization procedure of the generalized type in the sense of Rulkov et al [Phys. Rev. E 51, 980 (1995)] is used to impose a nonlinear Malasoma chaotic motion on the Frenet-Serret system of vectors in the differential geometry of space curves. This could have applications to the mesoscopic motion of biological filamentsComment: 12 pages, 7 figures, accepted at Int. J. Theor. Phy

An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces

The complex oscillatory behavior of a spring-block model is analyzed via the Hopf bifurcation mechanism. The mathematical spring-block model includes Dieterich–Ruina's friction law and Stribeck's effect. The existence of self-sustained oscillations in the transition zone – where slow earthquakes are generated within the frictionally unstable region – is determined. An upper limit for this region is proposed as a function of seismic parameters and frictional coefficients which are concerned with presence of fluids in the system. The importance of the characteristic length scale L, the implications of fluids, and the effects of external perturbations in the complex dynamic oscillatory behavior, as well as in the stationary solution, are take into consideration

Mutual information rate and bounds for it

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators

U.S. Natural Resources and Climate Change: Concepts and Approaches for Management Adaptation

Public lands and waters in the United States traditionally have been managed using frameworks and objectives that were established under an implicit assumption of stable climatic conditions. However, projected climatic changes render this assumption invalid. Here, we summarize general principles for management adaptations that have emerged from a major literature review. These general principles cover many topics including: (1) how to assess climate impacts to ecosystem processes that are key to management goals; (2) using management practices to support ecosystem resilience; (3) converting barriers that may inhibit management responses into opportunities for successful implementation; and (4) promoting flexible decision making that takes into account challenges of scale and thresholds. To date, the literature on management adaptations to climate change has mostly focused on strategies for bolstering the resilience of ecosystems to persist in their current states. Yet in the longer term, it is anticipated that climate change will push certain ecosystems and species beyond their capacity to recover. When managing to support resilience becomes infeasible, adaptation may require more than simply changing management practices—it may require changing management goals and managing transitions to new ecosystem states. After transitions have occurred, management will again support resilience—this time for a new ecosystem state. Thus, successful management of natural resources in the context of climate change will require recognition on the part of managers and decisions makers of the need to cycle between “managing for resilience” and “managing for change.

Secure multiple signal transmission using chaos synchronization

In this contribution we present the secure transmission of several signals based on chaos synchronization. The idea is to transmit as many signals as system states in secure manner. It is required that the transmitted chaotic attractor does not change in order to maintain the security level. The method is based on the Multiple-Input and Multiple-Output (MIMO) control theory for nonlinear systems. Moreover the Transmitter and Receiver synchronizes in spite of the uncertainties in both systems. In this sense the secure communication scheme is robust. We illustrate the result using synchronization of similar systems