Related papers: An analysis of the periodically forced PP04 climat…
We look at the periodic behaviour of the Earth's glacial cycles and the transitions between different periodic states when either external parameters (such as $\omega$) or internal parameters (such as $d$) are varied. We model this using…
We present a new conceptual model of the Earth's glacial-interglacial cycles, one leading to governing equations for which the vector field has a hyperplane of discontinuities. This work extends the classic Budyko- and Sellers-type…
Low-order climate models can play an important role in understanding low-frequency variability in the atmospheric circulation and how forcing consistent with anthropogenic climate change may affect this variability. Here, we study a…
The climate record preserved in polar glaciers, mountain glaciers, and widespread cave deposits shows repeated occurrence of abrupt global transitions between cold/dry stadial and warm/wet interstadial states during glacial periods. These…
The dynamics of glacial cycles is studied in terms of the dynamical systems theory. We explore the dependence of the climate state on the phase of astronomical forcing by examining five conceptual models of glacial cycles proposed in the…
We propose a conceptual model which generates abrupt climate changes akin to Dansgaard-Oeschger events. In the model these abrupt climate changes are not triggered by external perturbations but rather emerge in a dynamic self-consistent…
In latitude-dependent energy balance models, ice-free and ice-covered conditions form physical boundaries of the system. With carbon dioxide treated as a bifurcation parameter, the resulting bifurcation diagram is nonsmooth with curves of…
An important problem in modern applied science is characterizing the behavior of systems with complex internal dynamics subjected to external forcings from their environment. While a great variety of techniques has been developed to analyze…
This chapter is dedicated to the slow dynamics of the climate system, at time scales of one~thousand to one million years. We focus specifically on the phenomenon of ice ages that has characterised the slow evolution of climate over the…
Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as…
A system of nonlinear ordinary differential equations with forcing function is developed to model evolution processes in complex systems. In this system R, C, and P are the resource, consumption, and production functions correspondingly. F…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
The glacial cycles are attributed to the climatic response of the orbital changes in the irradiance to the Earth. These changes in the forcing are to small to explain the observed climate variations as simple linear responses. Non-linear…
We present a study of a delay differential equation (DDE) model for the Mid-Pleistocene Transition (MPT). We investigate the behavior of the model when subjected to periodic forcing. The unforced model has a bistable region consisting of a…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…
An intriguing problem in climate science is the existence of Earth's glacial cycles. We show that it is possible to generate these periodic changes in climate by means of the Earth's carbon cycle as the main determinant factor. The carbon…
Several complicated non-linear models exist which simulate the physical processes leading to fluctuations in global climate. Some of these more advanced models use observations to constrain various parameters involved. However, they tend to…
A review of the recent refereed literature fails to confirm quantitatively that carbon dioxide (CO2) radiative forcing was the prime mover in the changes in temperature, ice-sheet volume, and related climatic variables in the glacial and…
We study the behaviour at tipping points close to (smoothed) non-smooth fold bifurcations in one-dimensional oscillatory forced systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous…
Using an energy balance model with ice sheets, we examine the climate response of an Earth-like planet orbiting a G dwarf star and experiencing large orbital and obliquity variations. We find that ice caps couple strongly to the orbital…