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We propose a reduced form set of two coupled continuous time equations linking the price of a representative asset and the price of a bond, the later quantifying the cost of borrowing. The feedbacks between asset prices and bonds are mediated by the dependence of their fundamental values on past asset prices and bond themselves. The obtained nonlinear self-referencing price dynamics can induce, in a completely objective deterministic way, the appearance of periodically exploding bubbles ending in crashes. Technically, the periodically explosive bubbles arise due to the proximity of two types of bifurcations as a function of the two key control parameters $b$ and $g$, which represent, respectively, the sensitivity of the fundamental asset price on past asset and bond prices and of the fundamental bond price on past asset prices. One is a Hopf bifurcation, when a stable focus transforms into an unstable focus and a limit cycle appears. The other is a rather unusual bifurcation, when a stable node and a saddle merge together and disappear, while an unstable focus survives and a limit cycle develops. The lines, where the periodic bubbles arise, are analogous to the critical lines of phase transitions in statistical physics. The amplitude of bubbles and waiting times between them respectively diverge with the critical exponents $gamma = 1$ and $ u = 1/2$, as the critical lines are approached.
We present a methodology to extract the backbone of complex networks based on the weight and direction of links, as well as on nontopological properties of nodes. We show how the methodology can be applied in general to networks in which mass or ener
The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively
Modelling all possible life cycles of a company in a highly competitive economic environment gives a significant advantage to the owner in his business investment activities. This article proposes and analyses a dynamic model of a companys life cycle
The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, exto
We have conducted an agent-based simulation of chain bankruptcy. The propagation of credit risk on a network, i.e., chain bankruptcy, is the key to nderstanding largesized bankruptcies. In our model, decrease of revenue by the loss of accounts payabl