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In this paper, a new chaotic map is proposed, that is obtained from the composition of two chaotic maps, that is, the MS Map and the Dyadic Transformation Map. The composition process starts from the MS Map, followed by the Dyadic Transformation Map. The resulting composition is a new chaotic function. This is shown by the bifurcation diagram analysis result, Lyapunov Exponents, and the NIST randomness test. The bifurcation diagram shows that the best densities occur at λ ∈ (0.3, 5) and r = 3.8. The Lyapunov Exponents has nonnegative values for r ∈ [1, 4]. The NIST randomness test with initial value and parameters x 0 = 0.6, r = 3.8, and λ = 3.5 shows that the new chaotic map passes 14 out of 16 NIST tests.

Chaos based cryptography has becoming an interesting topic lately, as it utilizes chaotic systems properties for secure key concealment. Many chaotic functions are discovered, constructed, and used time over time for this purpose, which will be our main aim here. Two well known maps that has been known for exhibiting chaotic behaviors are the Gauss Map and the Circle Map, where the Circle Map has unlimited chaos potential, while the Gauss Map’s is much weaker and limited. In this paper, we investigate computationally using Python whether the Gauss Map can be improved by combining it with the Circle Map, allowing exploitation of greater chaotic behaviors. For this purpose, an improved version of the Gauss map is constructed, from which, we plot its bifurcation diagrams and Lyapunov exponents graphics, and show that it has a good potential to be a random number generator (RNG) using the NIST test, as these are the three main aspects of chaotic maps utilized in chaos based cryptography. The results obtained from this observation shows that composing the Circle Map into the Gauss Map, along with several manipulations, generates a significantly improved version of the Gauss Map, as it has a bifurcation diagram with much higher density, much higher Lyapunov exponents, and mostly better P-Values from the NIST tests, although it is still not fully suitable for a RNG. The manipulations done here, which aims to conserve the maps ranges to stay within the chaotic intervals and position the Circle Map to be the “variable” of the Gauss Map, allows the chaotic behaviors from the original maps to be bequeathed and strengthened in the new map.

A new chaotic map is proposed from the composition of the improved logistic map and the MS map. The composition is done by mapping the MS map first, where the result is then mapped by the improved logistic map. The new map as the result of the composition is chaotic. This is shown by the Lyapunov Exponent analysis, bifurcation diagrams, and the NIST randomness test. The Lyapunov Exponent results with x0 = 0.1 are non-negative for r ∈ [1,4]. Its bifurcation diagrams with p ∈ (0,4) has a better density at r ∈ 2.5. The new chaotic function also passes 10 out of 16 NIST test, with initial value and parameter values x0 = 0.1, r = 2.5, and p = 2.5.

In this research the composition of water masses in the North Sulawesi (Sangihe Talaud) waters as part of the Indonesian Throughflow is investigated and analysed by using the Optimum Multi Parameter Analysis (OMP). The data used is the World Ocean Atlas data (WOA 13) in 1° x 1° latitude longitude resolution. Main data are the salinity, temperature and pressure. The Optimum Multiparameter analysis was used to calculate the percentage of each water mass contribution in the study waters. The contributions are 20-60% at 200-500 m depth for The North Pacific Intermediate Water (NPIW), 90-100%at around 0-100 meters depth for The North Pacific Subtropical Water (NPSW),100%at 900-1500 meters depth for the South Pacific Intermediate Water (SPIW)and 80-100% at 1100-1500 meters depth for TheAntartic Intermediate Water (AAIW). Surprisingly, the South Pacific Subtropical Water (SPSW) does not have any contribution and largest heat content comes from the AAIW. Magnitudes for each heat content of water types calculated in this study for NPIW, NPSW, AAIW, SPSW, and SPIW are in the range of 1.5 × 1014∼ 1.7 × 1014 J/m2, 2 × 1012∼ 9.9 × 1012 J/m2, 2.7 × 1014∼ 3.1 × 1014 J/m2, 0 ∼ 4.3 × 1011 J/m2, and 1.8 × 1014∼ 2 × 1014 J/m2, respectively. Eventhough the AAIW has the lowest temperature range but its large contribution in the waters outnumbers the warmer water masses.