scholarly journals Coexisting Hidden and Self-Excited Attractors in an Economic Model of Integer or Fractional Order

2021 ◽  
Vol 31 (04) ◽  
pp. 2150062
Author(s):  
Marius-F. Danca
Keyword(s):  
Economic System ◽  
Fractional Order ◽  
Economic Model ◽  
Foreign Capital ◽  
Capital Inflow ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Integer Order ◽  
Coexistence Of Attractors ◽  
System Variables

In this paper, the dynamics of an economic system with foreign financing, of integer or fractional order, are analyzed. The symmetry of the system determines the existence of two pairs of coexisting attractors. The integer-order version of the system proves to have several combinations of coexisting hidden attractors with self-excited attractors. Because one of the system variables represents the foreign capital inflow, the presence of hidden attractors could be of real interest in economic models. The fractional-order variant presents another interesting coexistence of attractors in the fractional-order space.

scholarly journals D3 Dihedral Logistic Map of Fractional Order

2021 ◽  
Author(s):  
Marius-F. Danca ◽  
Nikolay Kuznetsov
Keyword(s):  
Bifurcation Diagram ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Logistic Map ◽  
System Stability ◽  
Hidden Attractors ◽  
Integer Order

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

scholarly journals Coupled Discrete Fractional-Order Logistic Maps

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2204
Author(s):  
Marius-F. Danca ◽  
Michal Fečkan ◽  
Nikolay Kuznetsov ◽  
Guanrong Chen
Keyword(s):  
Numerical Integration ◽  
Fractional Order ◽  
Chaotic Dynamics ◽  
Chaotic Map ◽  
Hidden Attractors ◽  
Fractional Difference ◽  
Coexistence Of Attractors ◽  
Dynamical Properties

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.

scholarly journals D3 Dihedral Logistic Map of Fractional Order

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 213
Author(s):  
Marius-F. Danca ◽  
Nikolay Kuznetsov
Keyword(s):  
Bifurcation Diagram ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Logistic Map ◽  
Numerical Results ◽  
System Stability ◽  
Hidden Attractors ◽  
Integer Order

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.

Foreign Capital Inflow and Financial Crisis in a Dynamic Model

2015 ◽  
Author(s):  
Gopal K. Basak ◽  
Pranab Kumar Das ◽  
Allena Rohit
Keyword(s):  
Financial Crisis ◽  
Dynamic Model ◽  
Foreign Capital ◽  
Capital Inflow

Chaos and coexisting attractors in glucose-insulin regulatory system with incommensurate fractional-order derivatives

2021 ◽  
Vol 143 ◽  
pp. 110575
Author(s):  
Nadjette Debbouche ◽  
A. Othman Almatroud ◽  
Adel Ouannas ◽  
Iqbal M. Batiha
Keyword(s):  
Fractional Order ◽  
Regulatory System ◽  
Coexisting Attractors

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

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