Ламинарный хаос в связанных системах с запаздыванием

The possibility of the existence of laminar chaos in coupled time-delayed feedback systems is investigated. The cases of unidirectional and mutual coupling of time-delay systems are considered. It is shown for the first time that laminar chaos can exist not only in a system with a variable delay time, but also in a system with a constant delay time, if it is coupled with a system in the regime of laminar chaos.

New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay

This paper is concerned with certain non-linear unperturbed and perturbed systems of integro-delay differential equations (IDDEs). We investigate fundamental properties of solutions such as uniformly stability (US), uniformly asymptotically stability (UAS), integrability and instability of the un-perturbed system of the IDDEs as well as the boundedness of the perturbed system of IDDEs. In this paper, five new and improved fundamental qualitative results, which have less conservative conditions, are obtained on the mentioned fundamental properties of solutions. The technique used in the proofs depends on Lyapunov-Krasovski functionals (LKFs). In particular cases, three examples and their numerical simulations are provided as numerical applications of this paper. This paper provides new, extensive and improved contributions to the theory of IDDEs.

Absolute Stability of Neutral Systems with Lurie Type Nonlinearity

The paper studies absolute stability of neutral differential nonlinear systems x ˙ ( t ) = A x t + B x t − τ + D x ˙ t − τ + b f ( σ ( t ) ) , σ ( t ) = c T x ( t ) , t ⩾ 0 $$ \begin{align}\dot x(t)=Ax\left ( t \right )+Bx\left ( {t-\tau} \right ) +D\dot x\left ( {t-\tau} \right ) +bf({\sigma (t)}),\,\, \sigma (t)=c^Tx(t), \,\, t\geqslant 0 \end{align} $$ where x is an unknown vector, A, B and D are constant matrices, b and c are column constant vectors, 𝜏 > 0 is a constant delay and f is a Lurie-type nonlinear function satisfying Lipschitz condition. Absolute stability is analyzed by a general Lyapunov-Krasovskii functional with the results compared with those previously known.

EXPONENTIAL STABILITY OF LAMINATED BEAM WITH CONSTANT DELAY FEEDBACK

In this article, we consider a system of laminated beams with an internal constant delay term in the transverse displacement. We prove that the dissipation through structural damping at the interface is strong enough to exponentially stabilize the system under suitable assumptions on delay feedback and coefficients of wave propagation speed.

How Much Is Financial Advice Worth? The Transparency-Revenue Tension in Social Trading

In social trading, less experienced investors (followers) are allowed to copy the trades of experts (traders) in real time after paying a fee. Such a copy-trading mechanism often runs into a transparency-revenue tension. On the one hand, social trading platforms need to release traders’ trades as transparently as possible to allow followers to evaluate traders accurately. On the other hand, complete transparency may undercut the platform’s revenue because followers can free ride. That is, followers can manually copy the trades of a trader to avoid paying the following fees. This study addresses this critical tension by optimizing the level of transparency through delaying the release of trading information pertaining to the trades executed by traders. We capture the economic impact of the delay using the notions of profit-gap and delayed-profit. We propose a mechanism that elucidates the economic effects of the profit-gap and delayed-profit on followers and, consequently, the amount of money following a trader: protection effect and evaluation effect. Empirical investigations find support for these two effects. We then develop a stochastic control formulation that optimizes platform revenue, where the control is the optimal delay customized at the trader level and calculated as a function of the current amount of money following a trader and the number of views on the trader’s profile page. The optimized revenue can be incorporated into an algorithm to provide a systematic way to infuse the platform’s goals into the ranking of the traders. A counterfactual study is conducted to demonstrate the performance of the optimal delay policy (versus a constant-delay policy) using data from a leading social trading platform operating in the foreign exchange market. This paper was accepted by Chris Forman, information systems.

Inverse spectral boundary problem Sturm Liouville type with constant delay and non-zero initial function

This paper is dedicated to solving of the direct and inverse spectral problem for Sturm Liouville type of operator with constant delay from 𝜋/2 to 𝜋, non-zero initial function and Robin’s boundary conditions. It has been proved that two series of eigenvalues unambiguously define the following parameters: delay, coefficients of delay within boundary conditions, the potential on the segment from the point of delay to the right-hand side of the distance and the product of the starting function and potential from the left end of the distance to the delay point.