相关论文: Second-Order, Dissipative T\^atonnement: Economic …

The t\^atonnement process and Smale's process are two classical approaches to compute market equilibrium in exchange economies. While the t\^atonnement process can be seen as a first-order method, Smale's process, being second-order, is…

In two previous papers the author developed a second-order price adjustment (t\^atonnement) process. This paper extends the approach to include both quantity and price adjustments. We demonstrate three results: a analogue to physical…

Analyzing simple and natural price-adjustment processes that converge to a market equilibrium is a fundamental question in economics. Such an analysis may have implications in economic theory, computational economics, and distributed…

We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the oscillator is equivalent to a Li\'enard system.…

Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations…

The notion that economies should normally be in equilibrium is by now well-established; equally well-established is that economies are almost never precisely in equilibrium. Using a very general formulation, we show that under dynamics that…

The paper develops a second-order time-domain moment matching framework for the structure-preserving model reduction of second-order dynamical systems of high dimension, avoiding the first-order double-sized equivalent system. The moments…

Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…

Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…

In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…

We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity…

T\^atonnement is a simple, intuitive market process where prices are iteratively adjusted based on the difference between demand and supply. Many variants under different market assumptions have been studied and shown to converge to a…

In this paper, we derive an accelerated continuous-time formulation of Adam by modeling it as a second-order integro-differential dynamical system. We relate this inertial nonlocal model to an existing first-order nonlocal Adam flow through…

Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…

The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…

The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…

We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…

This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated…

Based on a simple observation that a classical second order differential equation may be decomposed into a set of two first order equations, we introduce a Hamiltonian framework to quantize the damped systems. In particular, we analyze the…

In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly…