Multistability route in a PWL multi-scroll system through fractional-order derivatives

نویسندگان

چکیده

Recently, it was discovered that the use of fractional derivatives induces occurrence multistable states in PWL systems with multiple scrolls. In this paper, we show emergence a system and study route to transition from monostable behavior by reducing order derivative. Using bifurcation diagrams describe evolution attractor as consequence change derivative basins attraction, has path multistability reveals mechanism for behavior. The resulting dynamics shows coexistence up n + 2 attractors, where is number scrolls generated integer-order system, which been confirmed two different n-multi-scrolls systems. Moreover, existence uniqueness proved Poincaré sections, behaviors exist, coexist, are not section same solution.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system

This Letter initiates a hysteresis series switching approach for generating multi-directional multi-scroll chaotic attractors from a threedimensional linear autonomous fractional differential system, including 1-D n-scroll, 2-D (n×m)-grid scroll, and 3-D (n×m× l)-grid scroll chaotic attractors. The underlying dynamical mechanisms of a fractional differential hysteresis system are then further i...

متن کامل

VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators

Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs) for fast proto...

متن کامل

Synchronization and stabilization of Multi-scroll Integer and fractional Order Chaotic attractors Generated using trigonometric Functions

Sigmoidal functions are usually used to characterize the behavior of dynamical systems, in particular, for neural networks. Recently, multilevel piecewise linear functions have been employed in cellular neural networks (CNN). In this paper, we first use the inverse trigonometric function, tan−1(x), to generate a series of trigonometric functions to obtain one-, twoand three-directional multi-sc...

متن کامل

A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions

and Applied Analysis 3 Ta bl e 1: Fr ac tio na lo rd er de riv at iv es fo rs om ef un ct io ns . Fu nc tio ns Lfr ac tio na ld er iv at iv es x β , > − 1 x − α + β Γ ( 1 + β )

متن کامل

A fourth-order approximation of fractional derivatives with its applications

A fourth-order compact difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted Grunwald formulae combining the compact technique. The properties of proposed fractional difference quotient operator are presented and proved. Then the new approximation formula is applied to solving the space fractional diffusion equations. By the energy...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Chaos Solitons & Fractals

سال: 2022

ISSN: ['1873-2887', '0960-0779']

DOI: https://doi.org/10.1016/j.chaos.2022.112355