Related Experiment Video
Updated: Jul 4, 2025
08:03
Study of Protein Dynamics via Neutron Spin Echo Spectroscopy
Published on: April 13, 2022
2.1K
Studying changes in the dynamical patterns in two physical models involving new Caputo operator
1Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia; College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia.
Journal of Advanced Research
|February 2, 2024
Summary
A novel Caputo fractional operator introduces new chaotic dynamics in physical models. Adjusting its parameter generates complex attractors, unlike classic fractional operators which yield non-chaotic states.
Area of Science:
- Nonlinear Dynamics
- Fractional Calculus
- Physical Systems Modeling
Background:
- Understanding phase transitions in physical models is crucial for describing system dynamics.
- Fractional calculus offers advanced tools for modeling complex phenomena.
Purpose of the Study:
- Investigate the impact of a new Caputo fractional operator on the dynamics of two physical models.
- Explore the influence of a tunable fractional parameter on dynamical patterns.
Main Methods:
- Introduced a new Caputo fractional operator and its associated Riemann-Liouville fractional integral.
- Proved key properties and lemmas for the new fractional operator and integral.
- Analyzed the fractional modified autonomous Van der Pol-Duffing and Liu systems.
Main Results:
- The new fractional operator, with its additional parameter, induced diverse chaotic attractors.
- The fractional Van der Pol-Duffing system displayed one-band, double-band chaos, and periodic cycles.
- The fractional Liu system exhibited double scroll, self-excited, and hidden chaotic attractors.
Conclusions:
- The new Caputo fractional operator effectively generates complex chaotic dynamics in physical models.
- The operator's parameter is key to producing chaotic attractors, contrasting with classic operators.
Related Concept Videos
01:22Second Derivatives and Laplace Operator
1.2K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Consider a scalar function. The curl of its...
1.2K
01:17Kinematic Equations - II
9.5K
The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
9.5K
01:30Typical Model Studies
359
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
359
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
55
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
55
01:20Two-Dimensional Force System
909
A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:
909
01:18Second Order systems II
113
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
113