INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 7, Issue 4 (2) , April 2018 (Special Issue FBSA)

Pages: 56-64
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Analytical and numerical study of a nonlinear finance model via dynamical systems approach

Author: Ranjan Das

Category: Engineering, Science and Mathematics

Abstract:

A new N-donor bridging ligand, 2-[2-(pyridylamino)phenylazo]pyridine has been synthesized by cobalt mediated fusion of 2-aminopyridine on coordinated 2-(phenylazo)pyridine. The free ligand HL was isolated and characterized by X-ray. The pKa of the ligand was 8.6 ? 0.1. The reaction of ZnCl2 with the ligand produces a di-metallic complex, [Zn2Cl2(L)2] where two metal ions were bridged across the deprotonated ligand. The colour of the di-zinc complex was blue which was due to the long wavelength transition near 590 nm and assigned to intra-ligand ?* transition. Similarly, CdCl2.H2O and HgCl2 react instantaneously with the deprotonated ligand producing dimeric ink-blue complexes [Cd2Cl2(L)2] and [Hg2Cl2(L)2] respectively. X-ray structures of the two complexes were reported. The coordination sphere around each Cd(II) ion was a distorted square pyramidal. The geometry of each Hg(II) ion in the mercury complex was also distorted square based pyramid with the metal ions lying out of planes of the three nitrogen atoms of the chelating ligands. The separation between the two Hg(II) ions was within the sum of their van der Waals radii. The origin of the intense blue colour in these complexes was the intra-ligand transitions that occur near 615 nm. 1H NMR of Hg2Cl2L2.0.5H2O indicates that it undergoes exchange in solution with the coordinated ligands.

Keywords: Chaos; Complex financial system; Stability analysis; Relation coefficient; Bifurcation.