In this paper, we revisit the famous classical Samuelson's multiplier-accelerator model for national economy. We reform this model into a singular discrete time system and study its solutions. The advantage of this study gives a better understanding of the structure of the model and more deep...

In this work, we reconsider the dynamics of a few versions of the classical Samuelson's multiplier-accelerator model for national economy. First we recall that the classical one with constant governmental expenditure, represented by a linear second-order difference equation, is able to generate...

This paper extends the classical Samuelson multiplier-accelerator model for national economy. Actually, this new modeling structure removes the basic shortcoming of the original model producing stable business cycles when realistic values of the parameters (multiplier, accelerator) are entered...

In this article, we assume a union of countries where each national economy interacts with the others. We propose a new model where (a) delayed variables are incorporated into the system of equations and (b) the interaction element is restricted into the annual governmental expenditure that is...

In this paper, a general model is provided to evaluate a stock when the dividend growth rate is a discrete variable. This new dividend valuation model assumes that the dividend growth rate follows a finite state discrete time semi-Markov chain. An important consequence is that prices become...

We generalize the concept of symplectic maps to that of k- symplectic maps: maps whose kth iterates are symplectic. Similarly, k-symmetries and k-integrals are symmetries (resp. integrals) of the kth iterate of the map. It is shown that k-symmetries and k-integrals are related by the...

We investigate the generalisations of the Quispel, Roberts and Thompson (QRT) family of mappings in the plane leaving a rational quadratic expression invariant to the case of four variables. We assume invariance of the rational expression under a cyclic permutation of variables and we impose a...

Conolly et al. [Math. Scientist 22 (1997) 83–91] have obtained the transient distribution for a random walk moving on the integers -∞k∞ of the real line. Their analysis is based on a generating function technique. In this paper, an alternative technique is used to derive elegant explicit...

The main goal of this work is the development of the correct methodology of calculation of the Green's function of broken symmetry structures. The two methods were analysed and it was concluded that the direct method with the use of the translational operators is not convenient for the analyses...

A systematic investigation on the complete integrability of the nonautonomous discrete–discrete modified Korteweg–de Vries (ΔΔmKdV) and sine Gordon (ΔΔsG) mappings is presented using Lax pair technique and singularity confinement criteria. We derive conditions on the coefficients of Lax...