Previous Work: Nonlinear dynamics

(a) Early warning signals:


A clear lake can become turbid within few days, for the small and gradual increment of nutrient load in a lake. This transition occurs without showing any significant prior change in its turbidity. In order to achieve its previous state i.e. clear lake, it requires much more withdrawal of nutrient than the amount of nutrient causes transition. It means a huge cost is required to shift the lake to the previous state. In some systems the reversibility itself is impossible to achieve, the classic example is the Sahara desert,that used to be savanna around five thousand years ago. Such kind of transition can be observed in many other systems such as crash in financial market or the shift from savanna to desert. Hirota et al. 2009 Science paper suggests that savanna can have two possible alternative stable states, for gradual increment or decrement in rainfall, savanna can shift to tropical forest and desert respectively. A large human population, biodiversity and environment depends on the savanna, it is important to prevent such transitions. One of the possible way is to get an early warning signals at a sufficient pace to the critical point of such transitions, so that necessary preventive or damage control actions can be taken by ecosystem managers. Towards this, spatial variance, spatial skewness, spatial correlation and discrete Fourier transform have proposed as an early warning signals for regime shift based on mathematical models. We have designed a method and applied these early warning signals to the spatial data of African savanna.

Human Physiological System:

During induction of general anaesthesia, following transitions can be observed in brain:

  1. Loss of consciousness
  2. Recovery of consciousness

I did a preliminary investigation on the transition from unconscious to conscious state post anesthesia administered duration. From the few published studies data, it can be infer that such shifts may occur drastically. Shift from  unconscious to consciousness may be predicted by analysing state variable of consciousness i.e. the spike rate of ECoG. To test this, we required the human electrocorticogram (ECoG) data that we did not get. Thus we throwed the methods and plans in recycle bin. 😦

(b) Stable State Analysis (Probability Density Function):

This analysis has done on spatial tree cover and fire frequency data set. To find out how does ecosystem stable state i.e. savanna responds for the change in fire frequency, what is the interval of fire frequency at which bi-modality can be observed, and at what fire frequency does transition occur from savanna to tropical forest?

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