Mathematics – Dynamical Systems
Scientific paper
2011-09-28
Mathematics
Dynamical Systems
31 pages, 20 figures
Scientific paper
There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronization phenomenon. Here, we identify the type of such synchronization and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the Van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal, the traditional concepts of phase- or frequency-locking used to define synchronization to periodic forcing are inadequate. Instead, we explore a different concept of {\it generalized synchronization} in terms of (coexisting) synchronized solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronized solutions (paleoclimate histories). In this way, we uncover multistable synchronization at low forcing strength, and monostable or unique synchronization at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyze Lyapunov exponents (local stability), and basins of attraction (global stability). We find that even though synchronized solutions are stable on a long term, there exist short episodes of desynchronization where nearby climate trajectories diverge temporarily (for about 50 kyr). We also show that when a synchronized solution approaches the boundary of its basin of attraction, small perturbations may cause a jump to a different paeleoclimate history. Our study brings new insight into paleoclimate dynamics and reveals a possibility for the climate system to wander throughout different climatic histories related to preferential synchronization regimes on obliquity, precession or combinations of both, as environmental parameters varied throughout the history of the Pleistocene.
Crucifix Michel
Saedeleer B. de
Wieczorek Sebastian
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