State-dependent Impulse Research Articles

Modeling and Dynamic Analysis of Algae–Fish Model with Two State-Dependent Impulse Controls

Modeling and Dynamic Analysis of Algae–Fish Model with Two State-Dependent Impulse Controls

Linear and State-Dependent Impulse Responses in Agent-Based Models: A New Methodology and an Economic Application

Linear and State-Dependent Impulse Responses in Agent-Based Models: A New Methodology and an Economic Application

Frequency-domain modelling of reset control systems using an impulsive description

The ever-increasing industry desire for improved performance makes linear controller design run into fundamental limitations. Nonlinear control methods such as Reset Control (RC) are needed to overcome these. RC is a promising candidate since, unlike other nonlinear methods, it easily integrates into the industry-preferred PID design framework. Thus far, RC has been analysed in the frequency domain either through describing function analysis or by direct closed-loop numerical computation. The former computes a simplified closed-loop RC response by assuming a sufficient low-pass behaviour. In doing so it ignores all harmonics, which literature has found to cause significant modelling prediction errors. The latter gives a precise solution, but by its direct closed-loop computation does not clearly show how open-loop RC design translates to closed-loop performance. The main contribution of this work is aimed at overcoming these limitations by considering an alternative approach for modelling RC using state-dependent impulse inputs. This permits accurately computing closed-loop RC behaviour starting from the underlying linear system, improving system understanding. A frequency-domain description for closed-loop RC is obtained, which is solved analytically by using several well-defined assumptions. This analytical solution is verified using a simulated high-precision stage, critically examining sources of modelling errors. The accuracy of the proposed method is further substantiated using controllers designed for various specifications.

Analysis of impulse release of Wolbachia to control Nilaparvata lugens

Brown planthopper Nilaparvata lugens is a serious rice damaging pest and can transmit rice ragged stunt virus. A new biological control method for Nilaparvata lugens by using Wolbachia wStri has been successful in the laboratory. No matter using the strategy of population replacement or the strategy of population suppression to release Nilaparvata lugens infected with wStri, theoretical analysis shows that Nilaparvata lugens infected with wStri may eventually disappear after interacting with the wild Nilaparvata lugens, so the Nilaparvata lugens infected with wStri should be released several times. The question is when and how much to release. In this paper, we propose a population replacement model and a population suppression model with state-dependent impulse release. The existence and stability conditions of the corresponding periodic solutions for these two systems are obtained by applying the theory of semi-continuous dynamical system. We found that the defined evaluation index of wStri release time determines the property of the solutions of the systems. The growth period of Nilaparvata lugens infected with wStri is divided into several stages according to the evaluation index of wStri release time, and the release measures for different stages are put forward, especially the release strategy to make the wild Nilaparvata lugens extinct is discussed. Based on the concept of control degree, a more realistic control goal is also discussed, which is to keep the wild Nilaparvata lugens under a lower level within a finite time. Numerical simulation shows that the effective control has good robustness to the biological parameters of insect, and both strategies can effectively control the wild Nilaparvata lugens.

Limit cycles of a class of Liénard systems derived from state-dependent impulses

Discontinuous phenomena, in which objects may behave continuously and sometimes discretely are not only found in nature and under laboratory conditions but also in simple, familiar contexts. For example, this phenomenon is skillfully incorporated into the internal structure of mechanical wristwatches. Unless an extremely small amount of state-dependent impulse is applied intermittently, the reciprocating rotational movement of the balance and hairspring, which is the heart of the mechanical wristwatch, cannot be maintained. The small amount of state-dependent impulse, which is often overlooked, can make a significant difference; however, very few studies have examined this subject. This study assumes the underlying cause of discontinuous behaviors as impulses generated when an object reaches a particular state, assuming that the continuous behavior follows the Liénard system, which is widely studied in the field of electrical circuits. The main theorem provides the conditions under which the effect of the impulses causes a stable limit cycle in the Liénard system, even if no limit cycle exists when there are no impulses. The Poincaré–Bendixson theorem for discontinuous dynamical systems and phase plane analysis are used to prove the main theorem. Several examples and their simulations are provided to illustrate the main theorem.

The state-dependent impulsive control for a general predator–prey model

In this paper, a general predator–prey model with state-dependent impulse is considered. Based on the geometric analysis and Poincaré map or successor function, we construct three typical types of Bendixson domains to obtain some sufficient conditions for the existence of order-1 periodic solutions. At the same time, the existing domains are discussed with respect to the system parameters. Moreover, the Analogue of Poincaré Criterion is used to obtain the asymptotic stability of the periodic solutions. Finally, to illustrate the results, an example is presented and some numerical simulations are carried out.

The short-term effects of tax changes: The role of state dependence

This study evaluates how the state of the economy, as measured by the rate of unemployment, influences the short-term effects of tax changes on output and employment. I examine the effects of narratively identified tax changes by adopting two alternative approaches to estimating state-dependent impulse response functions that have been widely used in the recent literature. Both approaches suggest that short-term effects of tax changes on output and employment are smaller during times of higher unemployment. I argue that increased labor market slack and tighter credit conditions in contractionary periods can reduce the responsiveness of labor supply to changes in labor income taxes, resulting in smaller effects on output from tax changes.

Analysis of the impact of inflation expectations based on machine learning intelligent models

Our country’s economic growth is overly dependent on government investment, and bank credit and money supply lack a strict monitoring mechanism. Therefore, rapid economic growth is always accompanied by inflation risks. In order to study the effect of inflation impact analysis, based on machine learning algorithms, this paper combines artificial intelligence technology to analyze the impact of inflation expectations, and constructs the central bank information disclosure index and inflation expectations index. Moreover, this paper will perform ADF unit root test on the data. In addition, after confirming that the data is stable, this paper uses the Markov Regime Transfer Vector Autoregressive (MSVAR) model and state-dependent impulse response function to test and analyze the effect of China’s central bank communication in guiding the formation of inflation expectations. Through research, we can see that the machine learning algorithm constructed in this paper has significant effects, which can provide a reference for the analysis of the impact of inflation expectations.

Non-Linear Exchange Rate Pass-Through to Euro Area Inflation: A Local Projection Approach

How long does it take for exchange rate changes to pass through into inflation? Does it make a difference whether the exchange rate depreciates or appreciates? Do relatively large exchange rate changes entail more exchange rate pass-through? In this paper, we examine possible non-linearities in the transmission of exchange rate movements to import and consumer prices in all 19 euro area countries as well as the euro area as a whole from 1997 to 2019Q1. We extend a standard single-equation linear framework with additional interaction terms to account for possible non-linearities and apply local projections to obtain state-dependent impulse response functions. We find that (i) euro area consumer and import prices respond significantly to exchange rate movements after one year, responding more when the exchange rate change is relatively large; and (ii) euro appreciations and depreciations affect the level of euro area exchange rate pass-through in a symmetric fashion; (iii) for euro area countries results differ for import and consumer prices and across countries. JEL Classification: E31, F41

Stability Analysis of Impulsive Switched Time-Delay Systems With State-Dependent Impulses

This paper studies the stability for impulsive switched time-delay systems with state-dependent impulses. Since the impulses and the switches are not necessarily synchronous, we start from a stability analysis of impulsive switched time-delay systems with time-dependent impulses. Sufficient conditions are derived to guarantee the stability property, which extends the previous results for the synchronous switch and impulse case. For the state-dependent impulse case, using the B-equivalent method, impulsive switched time-delay systems with state-dependent impulses are transformed into impulsive switched time-delay systems with time-dependent impulses. The equivalence between the original system and the transformed system is established, and stability conditions are obtained for impulsive switched time-delay systems with state-dependent impulses. Finally, a numerical example is given to demonstrate the obtained results.

Is ECB Monetary Policy More Powerful During Expansions?

This paper tests whether the effects of ECB monetary policy vary over different phases of the business cycle. It uses local projections to estimate the state-dependent impulse responses of economic activity and prices to monetary policy shocks. These are identified through high-frequency financial market responses after Governing Council meetings. While the impact of monetary policy on economic activity is roughly similar during recessions and expansions, prices respond more strongly during booms. The result holds when the state of the economy is based on measures of resource utilization, rather than on GDP growth rates. Nominal wages also respond more strongly to monetary policy during expansions and when there is no slack in the economy. The empirical findings are consistent with the presence of downward rigidity on nominal wages.

Dynamic analysis of a prey\u2013predator model with state-dependent control strategy and square root response function

In this work, a prey-predator model with square root response function under a state-dependent impulse is proposed. Firstly, according to the differential equation geometry theory and the method of successor function, the existence, uniqueness and attractiveness of the order-1 periodic solution are analyzed. Then the stability of the order-1 periodic solution is discussed by the Poincaré criterion for impulsive differential equations. Finally, we show a specific example and carry out numerical simulations to verify the theoretical results.

Geometrical analysis and control optimization of a predator-prey model with multi state-dependent impulse

In this paper, a predator-prey model with Holling type-I functional response and multi state impulsive feedback control is established, where the intensity of pesticide spraying and the release amount of natural enemies are linearly dependent on the given threshold in the second impulse. Firstly, the existence of order-1 periodic solution of the system is investigated by successor functions and Bendixson theorem of impulsive differential equations, then the stability of periodic solutions is proved by the analogue of the Poincaré criterion. Furthermore, in order to reduce the actual total cost and obtain the best economic benefit, the optimal economic threshold is obtained, which provides the optimal strategy for the practical application. Finally, numerical simulations for specific examples are carried out to illustrate the feasibility of the above conclusions.

Non-Linear Exchange Rate Pass-Through in Emerging Markets

This paper estimates exchange rate pass-through to consumer prices in emerging markets focusing on non-linearities and asymmetries. We document non-linearities and asymmetries in the transmission of exchange rate fluctuations to prices using local projection techniques to obtain state dependent impulse responses in a panel of 28 emerging markets. We find significant evidence of non-linearities during episodes of depreciation greater than 10 and 20 percent. More specifically, we find that, after one month, the exchange rate pass-through coefficient is equal to 18 and 25 percent respectively, compared to a coefficient of 6 percent in the linear case. We also investigate the role of temporary vs. permanent shocks and the adoption of an inflation targeting regime in the transmission from exchange rate movements to prices. We perform a set of robustness checks, addressing the presence of outliers and potential endogeneity concerns.

Non-Linear Exchange Rate Pass-Through in Emerging Markets

This paper estimates exchange rate pass-through to consumer prices in emerging markets focusing on non-linearities and asymmetries. We document non-linearities and asymmetries in the transmission of exchange rate fluctuations to prices using local projection techniques to obtain state dependent impulse responses in a panel of 28 emerging markets. We find significant evidence of non-linearities during episodes of depreciation greater than 10 and 20 percent. More specifically, we find that, after one month, the exchange rate pass-through coefficient is equal to 18 and 25 percent respectively, compared to a coefficient of 6 percent in the linear case. We also investigate the role of temporary vs. permanent shocks and the adoption of an inflation targeting regime in the transmission from exchange rate movements to prices. We perform a set of robustness checks, addressing the presence of outliers and potential endogeneity concerns.

A constructive approach to boundary value problems with state-dependent impulses

We investigate the non-linear system of ordinary differential equationsu′(t)=f(t,u(t)),a.e.t∈[a,b],subject to the state-dependent impulse conditionu(t+)−u(t−)=γ(u(t−))fort∈(a,b)suchthatg(t,u(t−))=0and the linear two-point boundary conditionAu(a)+Cu(b)=d.Here, −∞<a<b<∞,f and γ are given continuous vector-functions, g is a continuous scalar function, A, C are constant matrices, and d is a constant vector. The instants of time t where the jump occurs are determined by the equation g(t,u(t−))=0 and, thus, are unknown a priori and essentially depend on the solution u. We discuss a reduction technique allowing one to combine the analysis of existence of solutions with an efficient construction of approximate solutions. At present, according to the authors’ knowledge, no numerical results for boundary value problems with state-dependent impulses are available in the literature.

Impulsive predator-prey model

In this paper we considered a predator-prey model with state-dependent impulse. We determine periodic solutions for the model without impulses and we prove the existence of nontrivial periodic solution in the case of impulse depending on the state of the model.

First-order nonlinear differential equations with state-dependent impulses

The paper deals with the state-dependent impulsive problem z ′ ( t ) = f ( t , z ( t ) ) for a.e. t ∈ [ a , b ] , z ( τ + ) − z ( τ ) = J ( τ , z ( τ ) ) , γ ( z ( τ ) ) = τ , ℓ ( z ) = c 0 , where [a,b]⊂R, c 0 ∈R, f fulfils the Carathéodory conditions on [a,b]×R, the impulse function is continuous on [a,b]×R, the barrier function γ has a continuous first derivative on some subset of ℝ and ℓ is a linear bounded functional which is defined on the Banach space of left-continuous regulated functions on [a,b] equipped with the sup-norm. The functional ℓ is represented by means of the Kurzweil-Stieltjes integral and covers all linear boundary conditions for solutions of first-order differential equations subject to state-dependent impulse conditions. Here, sufficient and effective conditions guaranteeing the solvability of the above problem are presented for the first time.MSC:34B37, 34B15.

A new approach to BVPs with state-dependent impulses

The paper deals with the second-order Dirichlet boundary value problem with one state-dependent impulse Proofs of the main results contain a new approach to boundary value problems with state-dependent impulses which is based on a transformation to a fixed point problem of an appropriate operator in the space . Sufficient conditions for the existence of solutions to the problem are given here. The presented approach can be extended to more impulses and to other boundary conditions. MSC:34B37, 34B15.

Optimization of Measure-Driven Hybrid Systems

We study an optimal control problem for a state-dependent impulse system described by a measure differential equation. A specific time reparameterization technique is developed to reduce the impulsive control problem to the one with bounded controls. Necessary conditions of optimality are obtained by interpreting the Maximum Principle in the reduced problem. An impulsive control improvement scheme is outlined. The results of numeric simulation are presented.