Teleconnection between the climates of the Polar Regions during the last ice age

Understanding the well-documented differences between Greenland and Antarctica's paleoclimate proxy time series in terms of the dynamic processes connecting the two Polar Regions would help develop a quantitative theory of polar climate teleconnections. Multiple conceptual models have been proposed to explain the polar climate time series relationship, and to extend Greenland climate records based on the much longer records from Antarctica. Here we compare the most relevant conceptual models proposed to characterize inter-polar teleconnections associated with these time series. We show that the polar synchronization model, which proposes that the climates of the Polar Regions were phase synchronized over most of the last ice age, shows better overall skill across the range of parameter space under test and provides a physical explanation of the polar teleconnection as the mutual synchronization of two nonlinear, coupled oscillators. Phase synchronization results when two or more nonlinear oscillators couple (in this case the two polar climates coupled through the ocean and atmosphere) and therein adjust their (initially different) natural rhythms to a common frequency and constant relative phase. Detailed analyses presented here show that the polar synchronization is a reliable framework to support further studies of polar climate teleconnections.

A Continuation Approach to the Periodic Boundary Value Problem for a Class of Nonlinear Coupled Oscillators with Potential Depending on Time

In this paper, we prove a new continuation theorem for the solvability of periodic boundary value problems for nonlinear vector equations. By applying the continuation theorem, we prove the existence of a periodic solution for a class of semi-linear weekly-coupled systems with time-dependent potential.

Out-of-unison resonance in weakly nonlinear coupled oscillators

Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems.