We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically us... more We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically using Picard’s and the general linear method (GLM). We use trapezoidal and triangular fuzzy numbers as the initial conditions. To demonstrate the efficiency of the proposed methods, the exact as well as the numerical solutions are presented numerically and graphically. In addition, a comparison is made between the results from applying the GLM and those obtained when applying the fifth order Runge–Kutta method as reported in the literature.
Ankara : Department of Mathematics and the Institute of Engineering and Sciences of Bilkent Unive... more Ankara : Department of Mathematics and the Institute of Engineering and Sciences of Bilkent University, 2000.
نظريات في نهايات سلاسل ماركوف المعدودة فير المتجانسة نقوم في هذا البحث بدراسة نهايات سلاسل ماركوف... more نظريات في نهايات سلاسل ماركوف المعدودة فير المتجانسة نقوم في هذا البحث بدراسة نهايات سلاسل ماركوف المعدودة غير المتجانسة حيث أثبتنا أنه اذا كان هناك متتالية من سلاسل ماركوف الاركوديكية فان تركيب من هذه العناصر يكون اركوديكي اذا كانت مجموعة الحلات منتهية ويكون التركيب كذلك في حالة أن تكون مجموعة الحالات غير منتهية ولكن تحت شرط إضافي. كما أثبتنا أن نهاية تركيب من متتالية عشوائية تكون اركوديكي ضعيف تحت شرط معين، وتحت نفس الشرط تكون نهاية تركيب من متتالية من سلاسل ماركوف الاستوكاستية المزدوجة هي اركوديكية. هذا البحث مرتب بالطريقة التالية: الجزء (1) -الجزء(4): نظرة عامة عن سلاسل ماركوف وتصنيفاتها. الجزء(5): -مقدمة عن سلاسل ماركوف غير المتجانسة. الجزء (6): أمثلة عن سلاسل ماركوف غير المتجانسة. الجزء(7): نظريات حول سلاسل ماركوف غير المتجانسة. الجزء(8): ملاحظات حول الموضوع.
In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The fuzzy... more In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The fuzzy derivatives are approximated using the generalized Hukuhara derivative. To execute the numerical simulation, we use the fuzzy Runge-Kutta method. The results obtained over time for the evolution and the population are presented numerically and graphically with some conclusions.
In a previous work, we introduced particular fuzzy numbers and discussed some of their properties... more In a previous work, we introduced particular fuzzy numbers and discussed some of their properties. In this paper we use the comparison method introduced by Dorohonceanu and Marin(5) to compare between these fuzzy numbers.
Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent Universit... more Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent University, 1996.
In this paper, depending on max-min composition, we study the Ergodicity of a particular class of... more In this paper, depending on max-min composition, we study the Ergodicity of a particular class of finite fuzzy Markov chains where the first row of the transition matrices consists of arbitrary values (between zero and 1) while the other rows’ entries are one in one place and zero elsewhere. Under certain conditions, we show that a fuzzy Markov chain in this class is Ergodic.
We consider a predator prey system with the functional response of the form θ(x) = arctan(ax); a ... more We consider a predator prey system with the functional response of the form θ(x) = arctan(ax); a > 0. The main concern in this paper is the existence of limit cycles for such system. A necessary and sufficient condition for the nonexistence of limit cycles is given for such system.
Interacting particle systems is a mature area of probability theory. In this work we consider sev... more Interacting particle systems is a mature area of probability theory. In this work we consider several kinds of Hamiltonians in one dimensional models. We explain how they can be treated as non-homogeneous Markov chains.
In this paper, depending on max-min composition, and continuing the work in [10], we study the Er... more In this paper, depending on max-min composition, and continuing the work in [10], we study the Ergodicity of a particular class of finite fuzzy Markov chains where the last row of the fuzzy transition matrices consists of arbitrary values (between zero and 1) while the other rows’ entries are one in one place and zero elsewhere. Under certain conditions, we show that a fuzzy Markov chain in this class is Ergodic. We do the same when the last row is replaced by any row.
We consider a predator prey system with the functional response of the form µ(x) = arctan(ax); a ... more We consider a predator prey system with the functional response of the form µ(x) = arctan(ax); a > 0. The main concern in this paper is the existence of limit cycles for such system. A necessary and sufficient condition for the nonexis- tence of limit cycles is given for such system.
Journal of Mahani Mathematical Research Center, 2013
In a previous work, we introduced particular fuzzy numbers and discussed some of their properties... more In a previous work, we introduced particular fuzzy numbers and discussed some of their properties. In this paper we use the comparison method introduced by Dorohonceanu and Marin[5] to compare between these fuzzy numbers.
We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically us... more We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically using Picard’s and the general linear method (GLM). We use trapezoidal and triangular fuzzy numbers as the initial conditions. To demonstrate the efficiency of the proposed methods, the exact as well as the numerical solutions are presented numerically and graphically. In addition, a comparison is made between the results from applying the GLM and those obtained when applying the fifth order Runge–Kutta method as reported in the literature.
Ankara : Department of Mathematics and the Institute of Engineering and Sciences of Bilkent Unive... more Ankara : Department of Mathematics and the Institute of Engineering and Sciences of Bilkent University, 2000.
نظريات في نهايات سلاسل ماركوف المعدودة فير المتجانسة نقوم في هذا البحث بدراسة نهايات سلاسل ماركوف... more نظريات في نهايات سلاسل ماركوف المعدودة فير المتجانسة نقوم في هذا البحث بدراسة نهايات سلاسل ماركوف المعدودة غير المتجانسة حيث أثبتنا أنه اذا كان هناك متتالية من سلاسل ماركوف الاركوديكية فان تركيب من هذه العناصر يكون اركوديكي اذا كانت مجموعة الحلات منتهية ويكون التركيب كذلك في حالة أن تكون مجموعة الحالات غير منتهية ولكن تحت شرط إضافي. كما أثبتنا أن نهاية تركيب من متتالية عشوائية تكون اركوديكي ضعيف تحت شرط معين، وتحت نفس الشرط تكون نهاية تركيب من متتالية من سلاسل ماركوف الاستوكاستية المزدوجة هي اركوديكية. هذا البحث مرتب بالطريقة التالية: الجزء (1) -الجزء(4): نظرة عامة عن سلاسل ماركوف وتصنيفاتها. الجزء(5): -مقدمة عن سلاسل ماركوف غير المتجانسة. الجزء (6): أمثلة عن سلاسل ماركوف غير المتجانسة. الجزء(7): نظريات حول سلاسل ماركوف غير المتجانسة. الجزء(8): ملاحظات حول الموضوع.
In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The fuzzy... more In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The fuzzy derivatives are approximated using the generalized Hukuhara derivative. To execute the numerical simulation, we use the fuzzy Runge-Kutta method. The results obtained over time for the evolution and the population are presented numerically and graphically with some conclusions.
In a previous work, we introduced particular fuzzy numbers and discussed some of their properties... more In a previous work, we introduced particular fuzzy numbers and discussed some of their properties. In this paper we use the comparison method introduced by Dorohonceanu and Marin(5) to compare between these fuzzy numbers.
Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent Universit... more Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent University, 1996.
In this paper, depending on max-min composition, we study the Ergodicity of a particular class of... more In this paper, depending on max-min composition, we study the Ergodicity of a particular class of finite fuzzy Markov chains where the first row of the transition matrices consists of arbitrary values (between zero and 1) while the other rows’ entries are one in one place and zero elsewhere. Under certain conditions, we show that a fuzzy Markov chain in this class is Ergodic.
We consider a predator prey system with the functional response of the form θ(x) = arctan(ax); a ... more We consider a predator prey system with the functional response of the form θ(x) = arctan(ax); a > 0. The main concern in this paper is the existence of limit cycles for such system. A necessary and sufficient condition for the nonexistence of limit cycles is given for such system.
Interacting particle systems is a mature area of probability theory. In this work we consider sev... more Interacting particle systems is a mature area of probability theory. In this work we consider several kinds of Hamiltonians in one dimensional models. We explain how they can be treated as non-homogeneous Markov chains.
In this paper, depending on max-min composition, and continuing the work in [10], we study the Er... more In this paper, depending on max-min composition, and continuing the work in [10], we study the Ergodicity of a particular class of finite fuzzy Markov chains where the last row of the fuzzy transition matrices consists of arbitrary values (between zero and 1) while the other rows’ entries are one in one place and zero elsewhere. Under certain conditions, we show that a fuzzy Markov chain in this class is Ergodic. We do the same when the last row is replaced by any row.
We consider a predator prey system with the functional response of the form µ(x) = arctan(ax); a ... more We consider a predator prey system with the functional response of the form µ(x) = arctan(ax); a > 0. The main concern in this paper is the existence of limit cycles for such system. A necessary and sufficient condition for the nonexis- tence of limit cycles is given for such system.
Journal of Mahani Mathematical Research Center, 2013
In a previous work, we introduced particular fuzzy numbers and discussed some of their properties... more In a previous work, we introduced particular fuzzy numbers and discussed some of their properties. In this paper we use the comparison method introduced by Dorohonceanu and Marin[5] to compare between these fuzzy numbers.
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introduced by Dorohonceanu and Marin[5] to compare between these fuzzy
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