# The Middle Pleistocene Transition by frequency locking and slow ramping of internal period

## TL;DR

This paper introduces the Ramping with Frequency Locking (RFL) mechanism, explaining the Middle Pleistocene Transition by slow internal period changes and frequency locking, accounting for abrupt glacial cycle length increases without requiring rapid external parameter shifts.

## Contribution

The paper proposes the RFL mechanism as a novel explanation for the MPT, linking slow internal period ramping with frequency locking to produce abrupt cycle length changes.

## Key findings

- RFL explains the MPT without rapid external changes.
- Frequency locking can produce abrupt cycle shifts with slow parameter variation.
- The scheme for detecting RFL in complex models is proposed.

## Abstract

The increase in glacial cycle length from approximately $41$ to on average $100$ thousand years around $1$ million years ago, called the Middle Pleistocene Transition (MPT), lacks a conclusive explanation. We describe a dynamical mechanism which we call Ramping with Frequency Locking (RFL), that explains the transition by an interaction between the internal period of a self-sustained oscillator and forcing that contains periodic components. This mechanism naturally explains the abrupt increase in cycle length from approximately $40$ to $80$ thousand years observed in proxy data, unlike some previously proposed mechanisms for the MPT. A rapid increase in durations can be produced by a rapid change in an external parameter, but this assumes rather than explains the abruptness. In contrast, models relying on frequency locking can produce a rapid change in durations assuming only a slow change in an external parameter. We propose a scheme for detecting RFL in complex, computationally expensive models, and motivate the search for climate variables that can gradually increase the internal period of the glacial cycles.