Complex Dynamics in a Model of Common Fishery Resource Harvested by Multiagents with Heterogeneous Strategy

In this paper, we formulate a dynamical model of common fishery resource harvested by multiagents with heterogeneous strategy: profit maximizers and gradient learners. Special attention is paid to the problem of heterogeneity of strategic behaviors. We mainly study the existence and the local stability of non-negative equilibria for the model through mathematical analysis. We analyze local bifurcations and complex dynamics such as coexisting attractors by numerical simulations. We also study the local and global dynamics of the exclusive gradient learners as a special case of the model. We discover that when adjusting the speed to be slightly high, the increasing ratio of gradient learners may lead to instability of the fixed point and makes the system sink into complicated dynamics such as quasiperiodic or chaotic attractor. The results reveal that gradient learners with high adjusting speed may ultimately be more harmful to the sustainable use of fish stock than the profit maximizers.

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Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

Mathematics ◽

10.3390/math8091458 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1458 ◽

Cited By ~ 1

Author(s):

Sameh S Askar ◽

Abdulrahman Al-Khedhairi

Keyword(s):

Complex Dynamics ◽

Market Competition ◽

Equilibrium Points ◽

Profit Maximization ◽

Stable Complex ◽

Global Dynamics ◽

Limited Information ◽

Critical Curves ◽

Local And Global Dynamics ◽

Realistic Situation

The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained.

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Modeling and Analysis of the Multiannual Cholera Outbreaks with Host-Pathogen Encounters

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420501205 ◽

2020 ◽

Vol 30 (08) ◽

pp. 2050120

Author(s):

Wenjing Zhang

Keyword(s):

Complex Dynamics ◽

Backward Bifurcation ◽

Global Dynamics ◽

Modeling And Analysis ◽

Local And Global Dynamics ◽

Model Dynamics ◽

Host Pathogen ◽

Necessary And Sufficient ◽

And Control ◽

Parameter Values

Re-emergence of cholera threatens people’s health globally. However, its periodic re-emerging outbreaks are still poorly understood. In this paper, we develop a simple ordinary differential equation (ODE) model to study the cholera outbreak cycles. Our model involves both direct (i.e. human-to-human) and indirect (i.e. environment-to-human) transmission routes, due to the multiple interactions between the human host, the pathogen, and the environment. In particular, we model the pathogen searching distance as a Poisson point process, and then formulate the host-pathogen encounter (HPE) rate. A thorough mathematical analysis is performed to investigate local and global dynamics of the model. Necessary and sufficient condition under which the backward bifurcation occurs is derived. Fold, Hopf, and Bogdanov–Takens bifurcations are studied with original model parameter values to reveal their relations with model behaviors. One- and two-dimensional bifurcation diagrams are provided to categorize model dynamics with respect to its parameter values. Analytical and numerical analyses show that our simple model is sufficient to exhibit complex epidemic patterns of cholera dynamics including bistability and annual and multiannual periodic outbreaks. Our result regarding the backward bifurcation and complex dynamics of cholera epidemics highlight the challenges in the prevention and control of the disease.

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Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function

Discrete Dynamics in Nature and Society ◽

10.1155/2012/536570 ◽

2012 ◽

Vol 2012 ◽

pp. 1-22 ◽

Cited By ~ 13

Author(s):

Serena Brianzoni ◽

Cristiana Mammana ◽

Elisabetta Michetti

Keyword(s):

Production Function ◽

Growth Model ◽

Discrete Time ◽

Production Functions ◽

Elasticity Of Substitution ◽

Global Dynamics ◽

Production Factors ◽

Local And Global Dynamics ◽

Complex Features

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings while assuming a nonconcave production function. We prove that complex features exhibited are related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions.

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The thalamic low-threshold Ca 2+ potential: a key determinant of the local and global dynamics of the slow (<1 Hz) sleep oscillation in thalamocortical networks

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2011.0126 ◽

2011 ◽

Vol 369 (1952) ◽

pp. 3820-3839 ◽

Cited By ~ 14

Author(s):

Vincenzo Crunelli ◽

Adam C. Errington ◽

Stuart W. Hughes ◽

Tibor I. Tóth

Keyword(s):

Action Potential ◽

Slow Oscillation ◽

Global Dynamics ◽

Action Potential Firing ◽

Local And Global Dynamics ◽

Up States ◽

Potential Firing ◽

Low Threshold

During non-rapid eye movement sleep and certain types of anaesthesia, neurons in the neocortex and thalamus exhibit a distinctive slow (<1 Hz) oscillation that consists of alternating UP and DOWN membrane potential states and which correlates with a pronounced slow (<1 Hz) rhythm in the electroencephalogram. While several studies have claimed that the slow oscillation is generated exclusively in neocortical networks and then transmitted to other brain areas, substantial evidence exists to suggest that the full expression of the slow oscillation in an intact thalamocortical (TC) network requires the balanced interaction of oscillator systems in both the neocortex and thalamus. Within such a scenario, we have previously argued that the powerful low-threshold Ca 2+ potential (LTCP)-mediated burst of action potentials that initiates the UP states in individual TC neurons may be a vital signal for instigating UP states in related cortical areas. To investigate these issues we constructed a computational model of the TC network which encompasses the important known aspects of the slow oscillation that have been garnered from earlier in vivo and in vitro experiments. Using this model we confirm that the overall expression of the slow oscillation is intricately reliant on intact connections between the thalamus and the cortex. In particular, we demonstrate that UP state-related LTCP-mediated bursts in TC neurons are proficient in triggering synchronous UP states in cortical networks, thereby bringing about a synchronous slow oscillation in the whole network. The importance of LTCP-mediated action potential bursts in the slow oscillation is also underlined by the observation that their associated dendritic Ca 2+ signals are the only ones that inform corticothalamic synapses of the TC neuron output, since they, but not those elicited by tonic action potential firing, reach the distal dendritic sites where these synapses are located.

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Bifurcation Analysis and Optimal Harvesting of a Delayed Predator–Prey Model

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127415500121 ◽

2015 ◽

Vol 25 (01) ◽

pp. 1550012 ◽

Cited By ~ 1

Author(s):

P. Tchinda Mouofo ◽

R. Djidjou Demasse ◽

J. J. Tewa ◽

M. A. Aziz-Alaoui

Keyword(s):

Natural Resource Management ◽

Optimal Control Theory ◽

Uniform Boundedness ◽

Optimal Harvesting ◽

Global Dynamics ◽

Saddle Node Bifurcation ◽

Predator Prey ◽

Predator Prey Model ◽

Local Bifurcations ◽

Prey Model

A delay predator–prey model is formulated with continuous threshold prey harvesting and Holling response function of type III. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The positive invariance of the non-negative orthant is proved and the uniform boundedness of the trajectories. Stability of equilibria is investigated and the existence of some local bifurcations is established: saddle-node bifurcation, Hopf bifurcation. We use optimal control theory to provide the correct approach to natural resource management. Results are also obtained for optimal harvesting. Numerical simulations are given to illustrate the results.

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COMPETITION AND COOPERATION ON PREDATION: BIFURCATION THEORY OF MUTUALISM

Journal of Biological System ◽

10.1142/s0218339021500030 ◽

2021 ◽

pp. 1-25

Author(s):

SRIJANA GHIMIRE ◽

XIANG-SHENG WANG

Keyword(s):

Quantitative Information ◽

Model Systems ◽

Exclusion Principle ◽

Positive Equilibrium ◽

Global Dynamics ◽

Severe Condition ◽

Predator Species ◽

Competition And Cooperation ◽

Local And Global Dynamics ◽

Predator Prey Models

In this paper, we investigate two predator–prey models which take into consideration hunting cooperation (i.e., mutualism) between two different predators and within one predator species, respectively. Local and global dynamics are obtained for the model systems. By a detailed bifurcation analysis, we investigate the dependence of predation dynamics on mutualism (cooperative predation). From our study, we prove that mutualism may enhance the survival of mutualist predators in a severe condition and break the competitive exclusion principle. We further provide quantitative information about how the cooperative predation (mutualism) may (i) establish multiple stability switches on the positive equilibrium; (ii) generate backward bifurcation on equilibria; (iii) induce supercritical or subcritical Hopf bifurcations; and (iv) establish bi-stability phenomenon between the predator-free equilibrium and a positive equilibrium (or a limit cycle).

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Local and global dynamics in collective movements of embryonic cells

Biosystems ◽

10.1016/j.biosystems.2018.09.011 ◽

2018 ◽

Vol 173 ◽

pp. 36-51 ◽

Cited By ~ 1

Author(s):

Lev V. Beloussov ◽

Tatiana G. Troshina ◽

Nadezhda S. Glagoleva ◽

Stanislav V. Kremnyov

Keyword(s):

Global Dynamics ◽

Embryonic Cells ◽

Local And Global Dynamics ◽

Collective Movements

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2. Pentecostal Megachurches in Jakarta: Class, Local, and Global Dynamics

Pentecostal Megachurches in Southeast Asia ◽

10.1355/9789814786898-005 ◽

2018 ◽

pp. 21-46

Keyword(s):

Global Dynamics ◽

Local And Global Dynamics

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Disequilibrium Pasar Ikan Laut Aceh

Jurnal Ekonomi Pembangunan Kajian Masalah Ekonomi dan Pembangunan ◽

10.23917/jep.v14i1.149 ◽

2013 ◽

Vol 14 (1) ◽

pp. 38

Author(s):

Asmawati Asmawati ◽

Nazamuddin Nazamuddin

Keyword(s):

Resource Utilization ◽

Supply And Demand ◽

Assessment Model ◽

Management Policy ◽

Fish Stock ◽

Fishery Resource ◽

Aceh Province ◽

The Indian Ocean ◽

Stock Depletion ◽

Malacca Strait

This study is an attempt to construct an assessment model for fishery resources by taking Aceh province as a case. The accuracy of assessment of sustainability in fishery resource utilization is crucial. An erroneous assessment may lead to a false management policy and thereby fish stock depletion may take place as a result. Three behavioral equations used in this study constitute supply and demand functions. A simultaneous equations system was applied to assess the sustainability of fishery resource utilization. The model also incorporated the possibility of relationship between two Aceh’s fishery areas and the possibility of disequilibrium fish market. The estimation results show that the Malacca Strait capture fishery market is in disequilibrium due to excessive demand. The Indian Ocean capture fishery supplies the consumption needs of the population on the Malacca Strait side and therefore significantly increases the supply in the later area.

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