scholarly journals Dynamic Ecological System Analysis

2018 ◽  
Author(s):  
Huseyin Coskun
Keyword(s):  
Dynamic System ◽  
Nonlinear Dynamic ◽  
System Analysis ◽  
Interspecific Interactions ◽  
Mathematical Framework ◽  
Holistic View ◽  
Quantitative Classification ◽  
Network Analyses ◽  
Compartmental Systems ◽  
Dynamic Measures

This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning methodologies through which compartmental systems are decomposed to the utmost level. The dynamic system and subsystem partitioning enable tracking the evolution of the initial stocks, environmental inputs, and intercompartmental system flows, as well as the associated storages derived from these stocks, inputs, and flows individually and separately within the system. Moreover, the transient and the dynamic direct, indirect, acyclic, cycling, and transfer (diact) flows and associated storages transmitted along a given flow path or from one compartment, directly or indirectly, to any other are analytically characterized, systematically classified, and mathematically formulated. Further, the article develops a dynamic technique based on the diact transactions for the quantitative classification of interspecific interactions and the determination of their strength within food webs. Major concepts and quantities of the current static network analyses are also extended to nonlinear dynamic settings and integrated with the proposed dynamic measures and indices within the proposed unifying mathematical framework. Therefore, the proposed methodology enables a holistic view and analysis of ecological systems. We consider that this methodology brings a novel complex system theory to the service of urgent and challenging environmental problems of the day and has the potential to lead the way to a more formalistic ecological science.

scholarly journals Static Ecological System Analysis

2018 ◽  
Author(s):  
Huseyin Coskun
Keyword(s):  
System Analysis ◽  
Interspecific Interactions ◽  
Ecological Systems ◽  
Mathematical Framework ◽  
The Novel ◽  
Holistic View ◽  
Network Analyses ◽  
Input And Output ◽  
Compartmental Systems

In this article, a new mathematical method for static analysis of compartmental systems is developed in the context of ecology. The method is based on the novel system and subsystem partitioning methodologies through which compartmental systems are decomposed to the utmost level. That is, the distribution of environmental inputs and intercompartmental system flows, as well as the organization of the associated storages generated by these flows within the system is determined individually and separately. Moreover, the transient and the static direct, indirect, acyclic, cycling, and transfer (diact) flows and associated storages transmitted along a given flow path or from one compartment, directly or indirectly, to any other are analytically characterized, systematically classified, and mathematically formulated. A quantitative technique for the categorization of interspecific interactions and the determination of their strength within food webs is also developed based on the diact transactions. The proposed methodology allows for both input- and output-oriented analyses of static ecological networks. The input- and output-oriented analyses are introduced within the proposed mathematical framework and their duality is demonstrated. Major flow- and stock-related concepts and quantities of the current static network analyses are also integrated with the proposed measures and indices within this unifying framework. This comprehensive methodology enables a holistic view and analysis of ecological systems.

scholarly journals Dynamic Ecological System Measures

2018 ◽  
Author(s):  
Huseyin Coskun
Keyword(s):  
System Analysis ◽  
Interspecific Interactions ◽  
Flow Distribution ◽  
Ecological System ◽  
Mathematical Framework ◽  
Activity Levels ◽  
Holistic View ◽  
Network Analyses ◽  
Dynamic Measures ◽  
Ecological Science

The system decomposition theory has recently been developed for the dynamic analysis of nonlinear compartmental systems. The application of this theory to the ecosystem analysis has also been introduced in a separate article. Based on this methodology, multiple new dynamic ecological system measures and indices of matrix, vector, and scalar types are systematically introduced in the present paper. These mathematical system analysis tools are quantitative ecological indicators that monitor the flow distribution and storage organization, quantify the direct, indirect, acyclic, cycling, and transfer (diact) effects and utilities of one compartment on another, identify the system efficiencies and stress, measure the compartmental exposures to system flows, determine the residence times and compartmental activity levels, and ascertain the system resilience and resistance in the case of disturbances. The proposed dynamic system measures and indices, thus, extract detailed information about ecosystems' characteristics, as well as their functions, properties, behaviors, and various other system attributes that are potentially hidden in and even obscured by data. A dynamic technique for the quantitative characterization and classification of main interspecific interactions and the determination of their strength within food webs is also developed based on the diact effect and utility indices. Moreover, major concepts and quantities in the current static network analyses are also extended to nonlinear dynamic settings and integrated with the proposed dynamic measures and indices in this unifying mathematical framework. Therefore, the proposed methodology enables a holistic view and analysis of ecological systems. We consider that the proposed methodology brings a novel complex system theory to the service of urgent and challenging environmental problems of the day and has the potential to lead the way to a more formalistic ecological science.

scholarly journals Static Ecological System Measures

2018 ◽  
Author(s):  
Huseyin Coskun
Keyword(s):  
System Analysis ◽  
Interspecific Interactions ◽  
Flow Distribution ◽  
Ecological Systems ◽  
Ecological System ◽  
Mathematical Framework ◽  
Activity Levels ◽  
Holistic View ◽  
Network Analyses ◽  
Comprehensive Framework

A new mathematical method for the static analysis of ecological systems has recently been developed by the author and was presented in a separate article. Based on this methodology, multiple new ecological system measures and indices of matrix, vector, and scalar types are systematically introduced in the present paper. These mathematical system analysis tools are quantitative ecological indicators that monitor the flow distribution and storage organization, quantify the direct, indirect, acyclic, cycling, and transfer (diact) effects and utilities of one compartment-- directly or indirectly--on another, and determine the residence times and compartmental activity levels. Major flow- and stock-related concepts and quantities of the current static network analyses are also integrated with the proposed measures and indices within this novel and unifying mathematical framework. This comprehensive framework enables a holistic view and analysis of static ecological systems. A quantitative technique for the classification and characterization of interspecific interactions and the determination of their strength within food webs is also developed. The proposed methodology allows for both input- and output-oriented analyses of ecological networks. The holistic perspective of the proposed methodology is extended further from the input-oriented to the output-oriented analysis. The proposed system measures and indices, thus, extract detailed information about ecosystems's characteristics, as well as their functions, properties, behaviors, and various other system attributes that are potentially hidden in and even obscured by data.

Research and Exploration of Volterra Series on Nonlinear System Identification and Modeling

2010 ◽  
Vol 439-440 ◽  
pp. 584-589 ◽  
Author(s):  
Y. Chen
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Dynamic System ◽  
Nonlinear Dynamic ◽  
System Analysis ◽  
Reproducing Kernel ◽  
Volterra Series ◽  
Kernel Method ◽  
Nonlinear System Identification ◽  
Nonlinear Dynamic System

With the development of analysis and identification way to nonlinear dynamic system, people uses many different method to build up mathematics model to simulate nonlinear dynamic system. This paper introduces some important nonlinear system identification ways and a kind of Volterra series expression type in detail. This kind of way adopts Hilbert reproducing kernel method to build up nonlinear dynamic system model. Hilbert space provides a kind of effective expression type for Fourier series and transfer based on anyorthogonal polynomial. Volterra series function has very strict theory basic, which can be applied into many nonlinear dynamic system analysis and identification filed, and has broad practicality and application prospect.

scholarly journals Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental Systems

2018 ◽  
Author(s):  
Huseyin Coskun
Keyword(s):  
Mathematical Method ◽  
Fundamental Matrix ◽  
Nonlinear Dynamic ◽  
System Analysis ◽  
Dynamic Method ◽  
Compartmental Systems ◽  
Mathematical System ◽  
Nonlinear Decomposition ◽  
And Storage ◽  
Decomposition Principle

A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning methodologies. A deterministic mathematical method is developed for the dynamic analysis of nonlinear compartmental systems based on the proposed theory. The dynamic method enables tracking the evolution of all initial stocks, external inputs, and arbitrary intercompartmental flows, as well as the associated storages derived from these stocks, inputs, and flows individually and separately within the system. The transient and the dynamic direct, indirect, acyclic, cycling, and transfer (diact) flows and associated storages transmitted along a particular flow path or from one compartment--directly or indirectly--to any other are then analytically characterized, systematically classified, and mathematically formulated. Thus, the dynamic influence of one compartment, in terms of flow and storage transfer, directly or indirectly on any other compartment is ascertained. Consequently, new mathematical system analysis tools are formulated as quantitative system indicators. The proposed mathematical method is then applied to various models from literature to demonstrate its efficiency and wide applicability.

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