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Justified Modeling Frameworks and Novel Interpretations of Ecological and Epidemiological Systems
  • Language: en
  • Pages: 151

Justified Modeling Frameworks and Novel Interpretations of Ecological and Epidemiological Systems

The Lotka-Volterra and the Kermack-McKendrick models are well celebrated and widely recognized in the field of ecology and epidemiology. Several modified ordinary differential equation models have been proposed over the last many decades to rationalize complex biological phenomena. In the current century, researchers have paid much attention to developing new modeling frameworks with delay differential equations, difference equations, fractional order systems, stochastic differential equations, etc. No doubt, these models have emerged many new bifurcations theory and methods which have equally contributed to the advances of Mathematics and interdisciplinary research. It is argued that these ...

Nonlinear Differential Equations and Dynamical Systems
  • Language: en
  • Pages: 158

Nonlinear Differential Equations and Dynamical Systems

  • Type: Book
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  • Published: 2021-04-15
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  • Publisher: MDPI

This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Matematika Keuangan
  • Language: id
  • Pages: 236

Matematika Keuangan

Buku Matematika Keuangan merupakan buku yang berisi tentang penjelasan secara teori matematis dan terapannya pada bidang keuangan. Buku Matematika Keuangan ini dirancang dengan sistematika penjelasan dan penggunaan bahasa yang runtun dan mudah dipahami oleh pembaca. Pada awal buku, pembaca disuguhkan secara detail konsep dasar bunga dan perhitungannya. Selain itu, teori matematis dan turunan serta keterkaitan antar rumus diulas dengan kalimat yang lugas dan mudah dipahami sehingga pembaca mampu memverbalkan tiap besaran dan angka yang diperoleh. Konsep lain yang dibahas secara detail pada buku ini dan menjadi dasar pemahaman kalkulasi transaksi keuangan adalah anuitas. Dasar-dasar teori bung...

Metode Numerik dengan MATLAB
  • Language: id
  • Pages: 268

Metode Numerik dengan MATLAB

Banyak masalah nyata seperti pada bidang statistika, aktuaria, teknik, ekonomi, biologi, pertanian, dan kimia dapat diilustrasikan dalam bentuk persamaan matematika, namun umumnya persamaan ini sulit diselesaikan secara analitik. Oleh karena itu, diperlukan suatu metode pendekatan untuk menyelesaikan masalah tersebut yang disebut dengan metode numerik. Buku ini disusun dengan tujuan untuk mempermudah mahasiswa dalam mempelajari mata kuliah Metode Numerik. Secara garis besar materi yang dibahas dalam buku ini memuat tentang galat, akar persamaan nonlinear, sistem persamaan linear, sistem persamaan nonlinear, pencocokan kurva, interpolasi, turunan, dan integral. Setiap materi diupayakan disaji...

The Logistic Map and the Route to Chaos
  • Language: en
  • Pages: 413

The Logistic Map and the Route to Chaos

Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

Nonstandard Finite Difference Models of Differential Equations
  • Language: en
  • Pages: 264

Nonstandard Finite Difference Models of Differential Equations

This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of ?exact? and ?best? finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation.

Optimal Control Applied to Biological Models
  • Language: en
  • Pages: 272

Optimal Control Applied to Biological Models

  • Type: Book
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  • Published: 2007-05-07
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  • Publisher: CRC Press

From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t

Mathematical Biology
  • Language: en
  • Pages: 551

Mathematical Biology

Mathematical Biology is a richly illustrated textbook in an exciting and fast growing field. Providing an in-depth look at the practical use of math modeling, it features exercises throughout that are drawn from a variety of bioscientific disciplines - population biology, developmental biology, physiology, epidemiology, and evolution, among others. It maintains a consistent level throughout so that graduate students can use it to gain a foothold into this dynamic research area.

Fractional-Order Nonlinear Systems
  • Language: en
  • Pages: 218

Fractional-Order Nonlinear Systems

"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to sim...

Nonlinear Dynamics of Interacting Populations
  • Language: en
  • Pages: 224

Nonlinear Dynamics of Interacting Populations

This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative theory of dynamical systems — most importantly bifurcation theory, which describes the dependence of ...