Related Experiment Video
Updated: Nov 27, 2025
06:14
Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface
Published on: July 30, 2020
5.2K
Coexisting Infinite Orbits in an Area-Preserving Lozi Map
Houzhen Li1, Kexin Li1, Mo Chen1
1School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study reveals initial value-dependent coexisting infinite orbits in the discrete Lozi map, including periodic, quasi-periodic, and chaotic behaviors. Complexity analysis confirms these orbits are intricately linked to initial conditions.
Area of Science:
- Dynamical systems and chaos theory.
- Nonlinear dynamics and discrete systems.
- Memristor-based circuit applications.
Background:
- Extreme multistability with coexisting infinite orbits is common in continuous memristor systems.
- Such phenomena are rarely observed in discrete dynamical systems.
- Understanding discrete systems is crucial for developing novel chaotic circuits.
Purpose of the Study:
- To investigate initial value-related coexisting infinite orbits in a discrete dynamical system.
- To analyze the complexity and topological characteristics of these orbits.
- To validate findings through a hardware implementation.
Main Methods:
- Utilized bifurcation and phase orbit diagrams to identify coexisting infinite orbits.
- Employed spectral entropy and sample entropy to quantify initial value-related complexity.
- Developed a microprocessor-based hardware platform for experimental validation.
Main Results:
- Discovered initial value-dependent coexisting infinite orbits in the area-preserving Lozi map.
- Identified diverse orbit types including periodic, quasi-periodic, and chaotic behaviors.
- Demonstrated complex complexity distributions intrinsically linked to initial values.
Conclusions:
- The area-preserving Lozi map exhibits significant initial value-related multistability in discrete systems.
- Coexisting infinite orbits display varied complexities dependent on initial conditions.
- Hardware validation confirms the theoretical findings on initial value sensitivity.
Related Concept Videos
01:26Areas Within Irregular Boundaries
220
Calculating areas within irregular boundaries, such as along rivers or curved roads, is crucial in various fields, including surveying, engineering, and environmental management. Surveyors often begin by creating a traverse, a connected series of straight lines approximating the area's boundary. The coordinates of each traverse point are essential for calculating the enclosed area. The double meridian distance formula is a widely used technique for this purpose. This method utilizes the...
220
01:24Area Computation by the Alternative Coordinate Method
350
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
350
01:20Region of Convergence of Laplace Tarnsform
914
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
914
02:33Lattice Centering and Coordination Number
10.8K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Types of Unit Cells
Imagine taking a large number of identical...
10.8K
01:19Limits with Oscillating Discontinuities
103
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
103
01:17Graphs of Polar Equations
101
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
101