Related Experiment Video
Updated: Nov 23, 2025
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
9.4K
Fractional q-deformed chaotic maps: A weight function approach
Guo-Cheng Wu1, Mehmet Niyazi Çankaya2, Santo Banerjee3
1Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, People's Republic of China.
Chaos (Woodbury, N.Y.)
|December 31, 2020
Summary
This study introduces fractional quantum calculus on the time scale to analyze chaotic dynamics in q-deformed discrete-time systems, overcoming challenges with non-local memory effects.
Area of Science:
- Nonlinear Dynamics
- Fractional Calculus
- Quantum Calculus
Background:
- Fractional derivatives model systems with long-range interactions and memory effects.
- Investigating chaos in deformed fractional discrete-time systems presents significant challenges due to non-locality.
Purpose of the Study:
- To explore chaotic dynamics in fractional q-deformed maps using fractional quantum calculus on the time scale.
- To propose an efficient methodology for modeling complex dynamics in such systems.
Main Methods:
- Application of fractional quantum calculus on the time scale.
- Utilization of discrete memory kernels.
- Development of a weight function approach for fractional modeling.
Main Results:
- Demonstration of rich q-deformed dynamics.
- Successful investigation of chaos in the studied fractional systems.
- Validation of the proposed methodology's efficiency.
Conclusions:
- Fractional quantum calculus on the time scale provides an effective framework for analyzing chaos in q-deformed discrete systems.
- The proposed weight function approach with discrete memory kernels is efficient for modeling complex dynamics.
Related Concept Videos
01:28Piecewise-Defined Functions
80
Piecewise defined functions are mathematical models where different expressions define a function over distinct intervals of the domain. These functions are useful for representing systems with varying behaviors depending on input values.For example, the function: uses a linear rule for inputs less than or equal to –1 and a quadratic rule for values greater than –1. Although it has two formulas, it still defines a single function.Another common type is the absolute value function, given...
80
01:28Partial Fractions
65
A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
65
01:20Inverse z-Transform by Partial Fraction Expansion
531
The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
To begin the process, the poles of the function are identified and the function is...
531
01:28Types of Functions III
76
Logarithmic and piecewise functions play central roles in mathematical modeling, particularly when capturing nonlinear or segmented behaviors in real-world phenomena. Although these functions differ fundamentally in structure and application, both serve to represent complex relationships in simplified mathematical terms.A logarithmic function is defined as the inverse of an exponential function, expressed as These functions grow quickly for small values of x but slow down as x increases,...
76
01:24Difference Equation Solution using z-Transform
502
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
502
01:29Transformations of Functions II
53
Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c,...
53