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The calcium oscillations have many important roles to perform many specific functions ranging from fertilization to cell death. The oscillation mechanisms have been observed in many cell types including cardiac cells, oocytes, and hepatocytes. There are many mathematical models proposed to describe the oscillatory changes of cytosolic calcium concentration in cytosol. Many experiments were observed in various kinds of living cells. Most of the experimental data show simple periodic oscillations. In certain type of cell, there exists the complex periodic bursting behavior. In this paper, we have studied further the fractional chaotic behavior in calcium oscillations model based on experimental study of hepatocytes proposed by Kummer et al. Our aim is to explore fractional-order chaotic pattern in this oscillation model. Numerical calculation of bifurcation parameters is carried out using modified trapezoidal rule for fractional integral. Fractional-order phase space and time series at fractional order are present. Numerical results are characterizing the dynamical behavior at different fractional order. Chaotic behavior of the model can be analyzed from the bifurcation pattern.

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In this paper we have formulated the stochastic search algorithm to solve classic constraint satisfaction problem (CSP) in mathematics 'N-queen problem'. This problem is a CSP that objects or states have to satisfy a number of constraints or criteria which have to place queens on the chessboard so that no queens attack each other. This problem is use as a benchmark to test search algorithms because the problem is difficult to search and there are many possible solutions. The stochastic search algorithm that we use is adapted the idea from condense matter physics called simulated annealing. The algorithm is widely use for solve many combinatorial optimization i.e., traveling salesman problem, wiring connection in electronics device, graph coloring. The theoretical analysis and experiment results show that acceptance ratio is converge to some constant.

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