If you start a journey from point A at time T1 and get to point B at time Tn. We say the "system" is linear if the arrival time is a function of the start time e.g. If you start at T1+1, you get there at time Tn+1 or generally, if you start at Ta+1 you arrive at Tn+a. Not all journey are smooth, there might be delay due to traffic and other unforeseen circumstances. Let's call the addition of all possible delay on the route d. If you take off at time T1, your arrival time due to delay on the route will be Tn+d. We refer to this "system" as a stochastic system. However, if the arrival time cannot be predicted based on the take off time T1 due to conditions around the starting conditions, we say the "system" is chaotic. Long term prediction of chaotic system is not possible. Chaos in this case does not mean random or disorder but sensitivity to initial starting conditions.
Chaos is aperiodic time-asymptotic behaviour in a deterministic system which exhibits sensitive dependence on initial conditions (http://farside.ph.utexas.edu/teaching/329/lectures/node57.html).
Initially, studying chaos was limited to complicated differential equations but in recent times, natural phenomena has been investigated for chaos. Many systems such as menstrual period (Derry and Derry, 2010), rainfall (Sivakumar, 2001), temperature (Fuwape et al, 2015), stock market (Fuwape and Ogunjo, 2013) have been found to be chaotic. To investigate chaos, tools such as correlation dimension, Lyapunov exponent, and other tools have been developed. Is chaos good or bad? This will be the subject of another post. In light of current agitation for use of renewable energy instead of fossil fuels, there is the need to study the predictability of the proposed energy systems.
Ogunjo, Adediji and Dada from the Department of Physics, Federal University of Technology, Akure investigated if solar radiation available at Akure, Southwestern Nigeria for a period of two years. The researchers found that the solar radiation at Akure during the dry season is more chaotic than during the wet season. This means that it is easier to predict the solar energy available in the location during the wet season than during the wet season of the year.
 |
| Figure 1: Phase space reconstruction of solar radiation data from Akure (Source: Ogunjo et al. 2014) |
The Nigerian government is currently on a drive to provide off-grid power based on solar energy. From the results presented by the researchers, it is imperative that the chaotic nature of solar energy over Nigeria be investigated and taken into consideration before large scale deployment. There is the need to further study the variation of incident solar radiation in different parts of the country for the most cost effective and reliable solar energy solution. For instance, further studies will give insight into the feasibility of combining solar energy with wind or other forms of energy for better reliability. Also, the possibility of solar panels that can track the rising and setting of the sun need to be investigated.
References
Derry, G., & Derry, P. (2010). Characterization of chaotic dynamics in the human menstrual cycle. Nonlinear Biomedical Physics, 4(1), 5. http://doi.org/10.1186/1753-4631-4-5
Fuwape, I. I. A., & Ogunjo, S. T. (2013). Investigating Chaos in the Nigerian Asset and Resource Management (ARM) Discovery Fund. CBN Journal of Applied Statistics, 4(2), 129–140. article.
Fuwape, I. A., Ogunjo, · S T, Oluyamo, · S S, Rabiu, · A B, (2016). Spatial variation of deterministic chaos in mean daily temperature and rainfall over Nigeria. Theoretical and Applied Climatology, In Press. http://doi.org/10.1007/s00704-016-1867-x
Ogunjo, S. T., Adediji, A. T., & Dada, J. B. (2015). Investigating chaotic features in solar radiation over a tropical station using recurrence quantification analysis. Theoretical and Applied Climatology. http://doi.org/10.1007/s00704-015-1642-4
Sivakumar, B. (2001). Is a chaotic multi-fractal approach for rainfall possible? Hydrological Processes, 15(6), 943–955. http://doi.org/10.1002/hyp.260
