5,427 research outputs found
Stability of stochastic impulsive differential equations: integrating the cyber and the physical of stochastic systems
According to Newton's second law of motion, we humans describe a dynamical
system with a differential equation, which is naturally discretized into a
difference equation whenever a computer is used. The differential equation is
the physical model in human brains and the difference equation the cyber model
in computers for the dynamical system. The physical model refers to the
dynamical system itself (particularly, a human-designed system) in the physical
world and the cyber model symbolises it in the cyber counterpart. This paper
formulates a hybrid model with impulsive differential equations for the
dynamical system, which integrates its physical model in real world/human
brains and its cyber counterpart in computers. The presented results establish
a theoretic foundation for the scientific study of control and communication in
the animal/human and the machine (Norbert Wiener) in the era of rise of the
machines as well as a systems science for cyber-physical systems (CPS)
Stabilisation of hybrid stochastic differential equations by delay feedback control
This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic differential equations (also known as stochastic dierential equations with Markovian switching) by delay feedback controls. Although the stabilisation by non-delay feedback controls for such equations has been discussed by several authors, there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap. To make our theory more understandable as well as to avoid complicated notations, we will restrict our underlying hybrid stochastic dierential equations to a relatively simple form. However our theory can certainly be developed to cope with much more general equations without any diculty
GAS STORAGE VALUATION UNDER LIMITED MARKET LIQUIDITY: AN APPLICATION IN GERMANY
Natural gas storages may be valuated by applying real options theory. However it is crucial, not to ignore that most evolving gas spot markets, like the German spot market, lack of liquidity. In this context, considering storage operators as price takers does not account for interdependencies of storage operations and market prices. This paper offers a novel approach to storage valuation taking into account the effect of management decisions on market prices. The within this paper proposed methodology determines the optimal production schedule and value by determining the stochastic differential equation describing the storage value and then applying a finite difference scheme. We find that limited liquidity lowers the storage value and reduces withdrawal and injection amounts. Further, we observe decreasing reservation prices for injection and withdrawing for growing illiquidity resulting in a left shift of injection and withdrawing threshold prices.natural gas valuation, limited liquidity
Edge of Chaos and Genesis of Turbulence
The edge of chaos is analyzed in a spatially extended system, modeled by the
regularized long-wave equation, prior to the transition to permanent
spatiotemporal chaos. In the presence of coexisting attractors, a chaotic
saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As
a control parameter is varied, the chaotic transient evolves to well-developed
transient turbulence via a cascade of fractal-fractal metamorphoses. The edge
state responsible for the edge of chaos and the genesis of turbulence is an
unstable travelling wave in the laboratory frame, corresponding to a saddle
point lying at the basin boundary in the Fourier space
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