Existence of chaos for partial difference equations via tangent and cotangent functions

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Conflicts of Interest

Identified Weaknesses

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Paper Summary

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Tangents and Cotangents Stir Up Chaos in Partial Difference Equations!

This paper introduces four chaotification schemes for partial difference equations involving tangent and cotangent functions. The schemes are shown to induce chaos in the sense of Li-Yorke or both Li-Yorke and Devaney, demonstrating how these trigonometric functions can be used as controllers to create chaotic behavior in such equations.

Possible Conflicts of Interest

None identified

Identified Weaknesses

Lack of Practical Applications

The paper focuses on establishing chaotification schemes for partial difference equations using tangent and cotangent functions, but the practical implications or applications of these schemes are not discussed. The lack of real-world context limits the impact and relevance of the findings.

Limited Examples

The paper heavily relies on theoretical proofs and mathematical derivations, but the provided examples are limited in scope and complexity. More diverse and complex examples are needed to showcase the robustness and effectiveness of the proposed schemes.

Superficial Analysis of Chaotic Dynamics

The paper claims the controlled systems exhibit "very complicated dynamical behaviors," but the analysis and interpretation of these behaviors are superficial. A deeper exploration of the chaotic dynamics, including quantifying the chaoticity and examining the long-term behavior, would strengthen the results.

Rating Explanation

This paper presents a solid theoretical framework for chaotifying partial difference equations using tangent and cotangent functions. The proofs are rigorous, and the examples, though limited, provide some illustration of the concepts. The lack of practical applications and in-depth analysis of chaotic dynamics prevents a higher rating.

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Topic Hierarchy

Domain:

Physical Sciences

Field:

Physics and Astronomy

Subfield:

Statistical and Nonlinear Physics

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Original Title:

Existence of chaos for partial difference equations via tangent and cotangent functions

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