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.

In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained.

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This paper is concerned with a class of discrete-time nonhomogeneous Markov jump systems with multiplicative noises and timevarying transition probability matrices which are valued on a convex polytope. The stochastic stability and finite-time stability are considered. Some stability criteria including infinite matrix inequalities are obtained by parameter-dependent Lyapunov function. Furthermore, infinite matrix inequalities are converted into finite linear matrix inequalities (LMIs) via a set of slack matrices. Finally, two numerical examples are given to demonstrate the validity of the proposed theoretical methods.

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Some mature reservoirs in China are encountering a sharp production decline, indicating a near-bleak production stabilizing prospect. Production fluctuation is essentially a phenomenon with a variety of affecting factors. An effective monitoring method has become a must with urgency for high water cut reservoirs. The existing development analyzing method or warning method is merely restricted to some particular indicator regarding development dynamics. However this kind of mechanism cannot be responsibly extended to continental deposited formations with strong heterogeneities for a lack of reliability and accuracy. In a reservoir engineering standpoint, all fluctuation in production can be feasibly traced from corresponding development dynamics indicators, which can change accordingly. Thus it is possible production change might be foreseen or predicted through analyzing the abnormal variations in indicators. We may start up analysis with oilfields and oil production plants owning sharp production variations, probe the causes behind and find the reflective indicators from 47 reservoirs. Our study has come up with a total of 10 perspective indicators for early warning, for instance, previous year oil rate ratio of new wells, ratio of oil rate from production enhancement, production injection ratio, enhancement efficiency and measurement Shortage, and the like. Various comparison and assessment standards are viable for different indicators. Oil production variations are further categorized into abnormal, normal, and better scenarios after evaluating uni-indicator using methods of plan comparison, trend comparison and history comparison without a neglect on individual indicator performance. Based on conventional warning strategies, a fresh early warning model with vector machine is devised. We apply this new model to 12 reservoirs in Shengli oilfield. Over 90% of abnormal production variations are successfully detected by this model through analyzing their nearly 20-year production history, yielding a practically good predicting accuracy and showcasing a big promise in effective monitoring for oil production.

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