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Exploring Neimark-Sacker Bifurcation and Chaos Control in a Tri-species discrete-time model

IRANIAN JOURNAL OF SCIENCE 2025年 1-21页

作者： Goldar, Sujay Hassan, Sk. Sarif Das, Krishna Pada Mohsen, Ahmed A. Bahlool, Dahlia Khaled Al-Mdallal, Qasem Rana, Sourav Gupta, Vikas Sardar, Purnendu Pingla Thana Mahavidyalaya Dept Math West Midnapore 721140 West Bengal India Mahadevananda Mahavidyalaya Dept Math Kolkata 700120 India Open Educ Coll Dept Math Baghdad Iraq Univ Baghdad Coll Sci Dept Math Baghdad Iraq UAE Univ Dept Math Sci Al Ain 17551 U Arab Emirates Visva Bharati Univ Dept Stat Santini Ketan 731235 West Bengal India LNM Inst Informat Technol Ctr Math & Financial Comp Dept Math Jaipur 302031 Rajasthan India Jadavpur Univ Ctr Math Biol & Ecol Dept Math 188 Raja SC Mallick Rd Kolkata 700032 India

This article presents a three-dimensional discrete-time ecological model to elucidate the intricate dynamics among three distinct species within an ecosystem. This approach extends traditional two-dimensional models, offering a more comprehensive perspective on ecological interactions. We identify all biologically feasible equilibria and perform a local stability analysis for each equilibrium point. Through bifurcation analysis (Neimark-Sacker and period-doubling bifurcations), we successfully demonstrate chaotic attractors via period doubling in the discrete-time model and implement chaos control through numerical simulations. By integrating this mathematical model, we derive ecological insights that contribute to informed conservation and management strategies, promoting sustainable biodiversity preservation.

关键词： Ecological dynamics discrete time model Stability analysis Neimark-Sacker bifurcation Period-doubling bifurcation Chaos

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The Interplay Between Dispersal and Allee Effects in a Two-Patch discrete-time model 27th

The Interplay Between Dispersal and Allee Effects in a Two-P...

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27th International Conference on Difference Equations and Applications (ICDEA)

作者： Ackleh, Azmy S. Veprauskas, Amy Univ Louisiana Lafayette Lafayette LA 70504 USA

ISBN: (纸本)9783031510519;9783031510496;9783031510489

We consider a discrete-time two-patch model with dispersal and a nonlinear non-monotone growth rate suggesting that the population in a patch may undergo an Allee effect. We assume that newborns do not disperse while other individuals in the population do. We first analyze the model without dispersal and demonstrate that, under certain conditions, the model exhibits two positive equilibria with both the extinction and larger positive equilibrium being locally asymptotically stable. We also provide conditions where a unique positive equilibrium exists and is globally asymptotically stable. We then study the model with dispersal and show that, if at least one patch undergoes an Allee effect in the absence of dispersal, then introducing dispersal may produce multiple stable positive equilibria. As a result, when dispersal parameters are varied, a discontinuous switching phenomenon between two attractors may be introduced into a patch that otherwise has continuous behavior. While the existence and stability of these equilibria is established theoretically for small dispersal proportions, it is shown through numerical simulation that this phenomena may also occur for large dispersal proportions.

关键词： discrete time model Dispersal Allee effect Multiple stable positive equilibria

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discrete time model of Coupled Inductor based Bidirectional DC-DC Converter 5

Discrete Time model of Coupled Inductor based Bidirectional ...

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5th International Conference on Electrical Energy Systems (ICEES)

作者： Madhuri, B. Krishna, D. S. G. VNR VJIET EEE Dept Hyderabad Telangana India

ISBN: (纸本)9781538692486

The present work emphasize on the small signal discrete averaged time model of a pulse width modulated coupled inductor based bidirectional dc-dc converter (CI-BDC). discrete averaged time model is used to predict the accurate model of the proposed converter in order to overcome the drawbacks of classical averaging techniques. Distinct behavior of converter is presented, when leading and trailing edge PWM techniques are applied. Proposed dc-dc converter is to avoid extreme values of duty ratio while coalescing low DC voltage sources with high DC voltage and to reduce the voltage and current(V/I) stress on the semiconductor devices of the power converter. A lead-lag compensation is introduced to avoid the instability due to right hand zero and better performance.

关键词： discrete time model Bidirectional converter Pulsewidth modulation Compensator

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A discrete-time model for Frequency Modulated Charge Pumps with Synchronized Controller 63

A Discrete-Time Model for Frequency Modulated Charge Pumps w...

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63rd IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)

作者： Tan, Yi Ishikuro, Hiroki Keio Univ Dept Elect & Elect Engn Yokohama Kanagawa Japan

ISBN: (纸本)9781728180588

This paper presents a discrete-time based approach for frequency modulated charge pumps with synchronized controller. In order to handle the varying frequency, this paper first introduced a method to calculate the output voltage of an open-loop charge pump with predefined frequencies, which is improved from a fixed frequency open-loop model verified in previous research. Then a closed-loop model is proposed for synchronized frequency controllers. An algorithm is hence created from the closed-loop model to simulate the output of charge pumps. The simulation result shows a competitive accuracy and much faster speed when comparing it with transistor level simulations. Overall, this paper demonstrated its value in terms of modeling the frequency modulated charge pumps and hence assisted the top-down design flow.

关键词： charge pumps circuit simulation discrete time model frequency modulation

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discrete time model of a two-station one-buffer serial system with inventory level-dependent operation

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COMPUTERS & INDUSTRIAL ENGINEERING 2017年 113卷 46-63页

作者： Gebennini, Elisa Grassi, Andrea Fantuzzi, Cesare Rimini, Bianca Univ Modena & Reggio Emilia Dipartimento Sci & Metodi Ingn Via Amendola 2 I-42122 Reggio Emilia Italy

The paper deals with the discrete-time discrete-state modeling of two-station one-buffer serial systems in which the condition of the first station (operative/idle) is controlled according to the inventory level of the intermediate buffer. Briefly, the first station is forced to remain idle each time the buffer fills up until it empties to a predefined inventory level (referred to as restarting-inventory level). Previous works have proved that this control policy, called restart policy, is effective when outage costs (e.g., waste production) are generated each time the first station restarts production after an interruption. While the works currently available in the literature assume that the buffer has to become completely empty before allowing the first station to resume production, the proposed paper develops a new analytical Markov model in which the restarting-inventory level can be greater than zero and arbitrarily set in the range [2, N-2], where N is the buffer size. The proposed model is solved in closed form by means of a partitioning procedure and a solution technique described in detail. Then, the most important performance measures are obtained as a function of the restarting-inventory level, *** size and the reliability parameters of both stations. Finally, some numerical results are discussed in order to validate the model and draw some concluding remarks about the values of the restarting-inventory level which maximize the effective efficiency of the system. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Transfer line discrete time model Control policy Restart level Performance analysis

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Grey Verhulst model and its chaotic behaviour with application to Bitcoin adoption

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DECISIONS IN ECONOMICS AND FINANCE 2022年第1期45卷 327-341页

作者： Gatabazi, P. Mba, J. C. Pindza, E. Univ Johannesburg Dept Math & Appl Math POB 524 ZA-2006 Auckland Pk South Africa Univ Rwanda Coll Business & Econ Sch Econ Dept Appl Stat POB 124 Huye Rwanda Univ Johannesburg Coll Business & Econ Sch Econ POB 524 ZA-2006 Johannesburg South Africa Tshwane Univ Technol Dept Math & Stat 175 Nelson Mandela Dr Private Bag X680 ZA-0001 Pretoria South Africa Univ Pretoria Dept Math & Appl Math Lynnwood Rd ZA-0002 Pretoria South Africa

The study applies the grey model (GM(1,1)) to the Verhulst differential equation for forecasting the Bitcoin transaction counts. The grey Verhulst model (GVM) is based on the data set of Bitcoin as recorded along 10 years from the 1st August 2010. The model accuracy is checked by the mean absolute percentage error (MAPE), while the model predictability is assessed by analysing a plot of the Verhulst model constructed upon the parameters provided by the GVM. The MAPE criterion suggests the reasonable accuracy of the overall GVM forecasting values and high accuracy by considering the last 400 forecasting values. Furthermore, the Verhulst model plot suggests that the GVM is potential on predictability as the plot is not chaotic. The GVM forecasting values suggest a slight future decline in transacting Bitcoin;this may be due to its competition with the other emerging cryptocurrencies. The GVM suggests a relatively high performance as compared to the usual one-variable forecasting model GM(1,1).

关键词： Grey model Mean absolute percentage error Continuous time model discrete time model Malthus model Verhulst model

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Echelon Base Stock Policy for Symbiotic and Reverse Logistic Flows 10th

Echelon Base Stock Policy for Symbiotic and Reverse Logistic...

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10th IFAC Triennial Conference on Manufacturing modelling, Management and Control (MIM)

作者： Hennequin, Sophie Yazdani, Mohammad Amin Roy, Daniel Univ Lorraine LGIPM Metz France

The main objective of this paper is to determine the base stock levels within the framework of an industrial symbiosis. At the operational level, we define the replenishment policies for finished and used products. The system is composed by two main warehouses and three enterprises located in the same industrial region, an eco-industrial park. For the first enterprise, we have two plants (or simply two manufacturing lines): the first plant manufactures finished products and the second one recovers used (wasted) finished products after collection and restores them. For the other enterprises, one enterprise consumes only finished products made by the first enterprise and the second one consumes by-products which could be used finished products or part of these used finished products coming from the second enterprise. This means that one enterprise consumes only finished products and generates wasted finished products and the second one could use these wasted finished products as inputs for its production. To simplify the study, we present only one kind of finished product but a generalization to several products and several customer and producer companies can simply be defined. The demands are uncertain such as the number of collected used finished products. The objective is then to define the base stock levels that minimize the long-run average expected total function, which is the sum of all economic, environmental and social costs. Numerical results are proposed to highlight our results. Copyright (C) 2022 The Authors.

关键词： Reverse logistic flows industrial symbiosis discrete time model replenishment policy echelon base stock

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Robustness of life histories to environmental variability in complex versus simple life cycles

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THEORETICAL ECOLOGY 2021年第2期14卷 335-344页

作者： Jonsson, Annie Univ Skovde Sch Biosci Ecol Modelling Grp S-54128 Skovde Sweden

Most animal species have a complex life cycle (CLC) with metamorphosis. It is thus of interest to examine possible benefits of such life histories. The prevailing view is that CLC represents an adaptation for genetic decoupling of juvenile and adult traits, thereby allowing life stages to respond independently to different selective forces. Here I propose an additional potential advantage of CLCs that is, decreased variance in population growth rate due to habitat separation of life stages. Habitat separation of pre- and post-metamorphic stages means that the stages will experience different regimes of environmental variability. This is in contrast to species with simple life cycles (SLC) whose life stages often occupy one and the same habitat. The correlation in the fluctuations of the vital rates of life stages is therefore likely to be weaker in complex than in simple life cycles. By a theoretical framework using an analytical approach, I have (1) derived the relative advantage, in terms of long-run growth rate, of CLC over SLC phenotypes for a broad spectrum of life histories, and (2) explored which life histories that benefit most by a CLC, that is avoid correlation in vital rates between life stages. The direction and magnitude of gain depended on life history type and fluctuating vital rate. One implication of our study is that species with CLCs should, on average, be more robust to increased environmental variability caused by global warming than species with SLCs.

关键词： Life histories Population growth rate Long-run growth rate Environmental variability Species life cycle discrete time model

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Simulating discrete time model Reference Adaptive Control System with Great Initial Error - Solution and Analysis 1

Simulating Discrete Time Model Reference Adaptive Control Sy...

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International Conference on Computer Applications Technology (ICCAT)

作者： Abushofa, Abubaker M. F. Azab, Abdel Hafez A. Univ Tripoli Dept Elect & Elect Engn Fac Engn Tripoli Libya

ISBN: (纸本)9781467352857

This article presents a discrete time model reference parameter tracking technique which is applicable for less order reference model, first introduced by A. A. Azab [8]. The order of the reference model is (n - l), where n is the number of the adjustable parameters in the physical plant. The technique utilizes a modified gradient method [9] where the knowledge of the exact order of the nonadaptive system is not required, so, as to eliminate the identification problem. Computer simulations for the solution and sensitivity analysis of one example are provided to demonstrate the simplicity and feasibility of the technique.

关键词： Adaptive Control System discrete Parameter Tracking discrete time model

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Unified discrete-time modeling and Digital Control of Bidirectional Chopper Converter 11

Unified Discrete-time Modeling and Digital Control of Bidire...

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11th International Conference on Power, Energy and Electrical Engineering (CPEEE)

作者： Jia, Yaoqin Jia, Biao Hou, Yijie Xiao, Junjie Zhao, Weiwei Huang, Po Xia, Anle Xi An Jiao Tong Univ Sch Elect Engn Xian Peoples R China

ISBN: (纸本)9781728177175

Bidirectional DC/DC converter is widely used in battery charge/discharge systems. The traditional state space average analysis method is not accurate enough when digital control is adopted. The separate analysis of the circuit from charge and discharge modes and design two sets of controllers will evidently reduce reliability and increase complexity of the system. Based on the discrete time modelling method, this paper establishes a unified discrete time model for current reversible chopper circuit. Then based on bilinear transformation method, design digital PI controller that can be directly applied according to the frequency domain index. By utilizing a unified current controller, accurate, fast and stable constant current charging/discharging control and switch can be realized. Voltage controller is used to realize constant voltage charging control. Finally, the validity and accuracy of the unified discrete-time model, unified current control strategy and digital controller design method proposed in this paper are further verified by simulation and experiments.

关键词： Bidirectional DC/DC converter digital control discrete time model

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