Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

In this paper, the complex dynamic behavior of a mixed duopoly game model is studied. Based on the principle of relative profit maximization and bounded rational expectation, the corresponding discrete dynamic systems are constructed in the case of nonlinear cost function. In theory, the conditions for the local stability of Nash equilibrium are given. In terms of numerical experiments, bifurcation diagrams are used to depict the effects of product differences, adjustment speed, and other parameters on the stability of Nash equilibrium.

Lifted Bayesian Filtering in Multiset Rewriting Systems

We present a model for Bayesian filtering (BF) in discrete dynamic systems where multiple entities (inter)-act, i.e. where the system dynamics is naturally described by a Multiset rewriting system (MRS). Typically, BF in such situations is computationally expensive due to the high number of discrete states that need to be maintained explicitly. We devise a lifted state representation, based on a suitable decomposition of multiset states, such that some factors of the distribution are exchangeable and thus afford an efficient representation. Intuitively, this representation groups together similar entities whose properties follow an exchangeable joint distribution. Subsequently, we introduce a BF algorithm that works directly on lifted states, without resorting to the original, much larger ground representation. This algorithm directly lends itself to approximate versions by limiting the number of explicitly represented lifted states in the posterior. We show empirically that the lifted representation can lead to a factorial reduction in the representational complexity of the distribution, and in the approximate cases can lead to a lower variance of the estimate and a lower estimation error compared to the original, ground representation.

Vibration Isolation Using Continuous Beams

Vibration Isolation involves an inertially coupled system with a mass-lever combination where the inertial forces cancel spring induced forces, thus permitting a high degree of isolation at a relatively low frequency in discrete dynamic systems. This paper shows that the lever combination can be clamped at the root rather than pinned and modeled as a continuous dynamic system. It is theoretically proven that this model can be tuned to achieve isolation with zero displacement, force, and moment transmissibility. The frequency response is calculated based on Euler Bernoulli assumptions for a beam with a tip mass under point force loading. A tip mass equivalent to the mass of the beam can reduce the first isolation frequency by 71% for shear at the root, 72% for moment at the root, and 64% for tip displacement, relative to a cantilever without a tip mass.

Dynamic systems for the analysis of the behavior of geosynthetics in railway engineering structures

While interacting with the elements of the engineering structures, geosynthetics can be treated as elastic membranes or shells placed on different types of foundation. Modeling of the real system takes into account the most important properties of the system and its elements. We will develop a physical and mathematical model in a form of generalized dynamic system. The mathematical description will use different operators leading to a continuous distributed system. The modeling will be further modified by development of discrete dynamic systems, which is enabled by the theory of generalized dynamic systems. This approach allows for the analysis of the problem with continuous and discrete signals. The results will show the response of the analyzed systems with analytic, numerical or hybrid methods.