I am trying to understand climate tipping points better and am looking for a place to ask the following question. If Mathematics SE isn't the right place, a recommendation of a better place would be welcome.
Let me refer to the paper Analysis and Predictability for Tipping Points with Leading-Order Nonlinear Terms and consider the dynamical system described by this set of stochastic differential equations:
$$\dot{T} = f(C,\dot{C}) + \sigma(T)\cdot\dot{W}$$
$$\dot{C} = g(T) + \varepsilon$$
with $T$ the mean global temperature, $C$ the mean concentration of atmospheric carbondioxide, $\sigma$ the $T$-dependent noise level, $W$ a one-dimensional Brownian motion, and $\varepsilon$ the (small) anthropogenic increase of atmospheric carbondioxide.
The function $f(C,\dot{C})$ captures the increase of $T$ by increasing $C$. When doubling of $C$ compared to $C_0 = 200\ \textsf{ppm}$ in 1850 or so results in an increase of $T$ by $3°C$, $f(C,\dot{C})$ takes the form
$$f(C,\dot{C}) = 3\cdot\dot{C}/C$$
The function $g(T)$ captures the fact, that the oceans emit an increasing net amount of $C$, depending on temperature. Let's assume that
$$g(T) = \gamma\cdot(T - T_0)$$
with $T_0$ the mean global temperature in 1850 or so.
The function $\sigma(T)$ captures the stochastic variance of temperature by internal variability which itself depends on the temperature. It may be assumed as
$$\sigma(T) = \sigma_0 + \sigma_1\cdot(T - T_0).$$
Question 1: Is the given form of $f(C,\dot{C})$ roughly correct? Which functions $g(T)$ and $\sigma(T)$ would be more realistic?
Question 3: What can be said about attractors and long-term behaviour of this system?
Question 3: Can this dynamical system give rise to tipping points?