The title thiocyanate-bridged dinuclear copper(II) complex, [Cu2(C12H17N2O2)2(NCS)2], possesses crystallographic inversion symmetry. Each CuII atom is five-coordinated by one imine N, one amine N and one phenolate O atom of the Schiff base ligand, and by two N atoms from two bridging thiocyanate ligands, forming a square-pyramidal geometry. Beside the two thiocyanate bridges, there are two intramolecular N—H⋯O hydrogen bonds, which further link the two Cu(C12H17N2O2)(NCS) units. The Cu⋯Cu separation is 3.261 (2) Å. Parts of the methylaminopropylimino segment are disordered over two sites with occupancies of 0.669(9) and 0.331(9).
We established a dynamic duopoly game model with consumer surplus and isoelastic demand, and studied the local and global dynamic characteristics of the game model. The local stability of the boundary equilibrium point is examined by way of the stability theory and Jacobian matrix, and through the Jury criterion, the stable region of the Nash equilibrium point is determined. The analysis revealed that the system may lose stability via the Flip bifurcation and the Neimark-Sacker bifurcation. The effect of each parameter on the stability of the system is discussed in virtue of numerical simulations, and it is concluded that when enterprises choose relatively small the speed of adjustment, profit weight coefficient and marginal cost, as well as relatively large price elasticity coefficient, it is more beneficial to the future long-term development of enterprises. With the help of the basin of attraction, the problem of attractor coexistence is studied. Multiple stability always implies path dependence, implying that historical chance has a significant impact on the future behavior of enterprises. In other words, the slight perturbations of the initial conditions will have a significant impact on how the system develops. In addition, we investigate the system’s global dynamical behavior using critical curves, basins of attraction, attracting areas and the noninvertible map, and discover three global bifurcations of the system. The boundary of the chaotic attractor and the region with higher density of points are given by the critical curve.
A dynamic oligopoly game model with nonlinear cost and strategic delegation is built on the basis of isoelastic demand in this paper. And the dynamic characteristics of this game model are investigated. The local stability of the boundary equilibrium points is analyzed by means of the stability theory and Jacobian matrix, and the stability region of the Nash equilibrium point is obtained by Jury criterion. It is concluded that the system may lose stability through Flip bifurcation and Neimark–Sacker bifurcation. And the effects of speed of adjustment, price elasticity, profit weight coefficient and marginal cost on the system stability are discussed through numerical simulation. After that, the coexistence of attractors is analyzed through the basin of attraction, where multiple stability always means path dependence, implying that the long-term behavior of enterprises is strongly affected by historical contingency. In other words, a small perturbation of the initial conditions will have a significant impact on the system. In addition, the global dynamical behavior of the system is analyzed by using the critical curves, the basin of attraction, absorbing areas and a noninvertible map, revealing that three global bifurcations, the first two of which are caused by the interconversion of simply-connected and multiply-connected regions in the basin of attraction, and the third global bifurcation, that is, the final bifurcation is caused by the contact between attractors and the boundary of the basin of attraction.
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