Fractional order chaotic systems: history, achievements, applications, and future challenges

MS Tavazoei - The European Physical Journal Special Topics, 2020 - Springer
Motivated by the importance of study on the complex behaviors, which may be exhibited by
fractional order differential equations, this review paper focuses on dynamical fractional …

A robust computational algorithm of homotopy asymptotic method for solving systems of fractional differential equations

Z Odibat, S Kumar - Journal of Computational and …, 2019 - asmedigitalcollection.asme.org
In this paper, we present new ideas for the implementation of homotopy asymptotic method
(HAM) to solve systems of nonlinear fractional differential equations (FDEs). An effective …

On the dynamics, control and synchronization of fractional-order Ikeda map

A Ouannas, AA Khennaoui, Z Odibat, VT Pham… - Chaos, Solitons & …, 2019 - Elsevier
This paper is concerned with a fractional Caputo-difference form of Ikeda map. The
dynamics of the proposed map is investigated numerically through phase plots and …

Nonlinear dynamics and chaos in fractional differential equations with a new generalized Caputo fractional derivative

Z Odibat, D Baleanu - Chinese Journal of Physics, 2022 - Elsevier
In this paper, novel systems of fractional differential equations involving a new generalized
Caputo fractional derivative were proposed. The complex dynamic behavior of these …

A new fractional-order chaotic system with different families of hidden and self-excited attractors

JM Munoz-Pacheco, E Zambrano-Serrano, C Volos… - Entropy, 2018 - mdpi.com
In this work, a new fractional-order chaotic system with a single parameter and four
nonlinearities is introduced. One striking feature is that by varying the system parameter, the …

Mode selection and stability of attractors in Chua circuit driven by piezoelectric sources

F Yang, J Ma, X An - Chaos, Solitons & Fractals, 2022 - Elsevier
The piezoelectric ceramic can be activated to produce continuous voltage and it is often
used to excite nonlinear circuits, which is tamed as functional circuit to detect the acoustic …

Firing activities of a fractional-order FitzHugh-Rinzel bursting neuron model and its coupled dynamics

A Mondal, SK Sharma, RK Upadhyay, A Mondal - Scientific reports, 2019 - nature.com
Fractional-order dynamics of excitable systems can be physically described as a memory
dependent phenomenon. It can produce diverse and fascinating oscillatory patterns for …

High speed FPGA-based chaotic oscillator design

M Tuna, M Alçın, İ Koyuncu, CB Fidan… - Microprocessors and …, 2019 - Elsevier
In this study, autonomous Lü-Chen (2002) chaotic system has been implemented on FPGA
using Heun numerical algorithm in VHDL 32-bit IQ-Math fixed-point number format for …

Chaotic characteristic analysis of network traffic time series at different time scales

Z Tian - Chaos, Solitons & Fractals, 2020 - Elsevier
Characteristic analysis of network traffic time series is very meaningful for network traffic
prediction. The dynamic behavior of network traffic time series is an external manifestation …

FPGA-based implementation of different families of fractional-order chaotic oscillators applying Grünwald–Letnikov method

AD Pano-Azucena, B Ovilla-Martinez… - … in Nonlinear Science …, 2019 - Elsevier
Fractional-order chaotic oscillators are a hot topic of research and nowadays many new
mathematical models have been introduced, which can be suitable for the development of …