Special Issue

Volume: 6 Issue: 2, 6/30/24

Year: 2024

Research Articles

Research Article

2. Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System

The journal aims to promote original research papers in the area of Chaos Theory and Applications (CHTA) to include practical innovations in Applied Sciences and Engineering. The journal aims to publish in as much detail as possible scientific advances in the field of chaos theory and applications with a focus on the practical and theoretical.

The journal publishes regular papers dealing with the following areas, but not limited to:


  • Chaos theory and chaotic systems,
  • Recent developments in chaos-based engineering applications,
  • Chaos in finance and blockchain,
  • Fractional-order chaotic systems,
  • Design of analogue circuits of chaotic systems,
  • Mem-elements-based systems,
  • Chaos-based embedded system applications,
  • Deterministic and random vibrations,
  • Mathematical modelling and chaos analysis in engineering,
  • Complexity in physical, social and biological systems,  
  • Applications to biomedical, data security, control, 
  • Chaos and its dynamics in biological networks,
  • Chaos and complexity in education,
  • Applications in astrophysics, space, geophysics, theoretical and structural chemistry, biophysics, social systems, power grids, image and time series processing.

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                Research Areas (Categories / Classification) 

  • Life Sciences & Biomedicine: Mathematical & Computational Biology, Life Sciences Biomedicine Other Topics.
  • Physical Sciences: Chemistry, Mathematics, Physics, Optics.
  • Social Sciences: Business & Economics, Social Sciences Other Topics.
  • Technology: Automation & Control Systems, Computer Science, Engineering, Mechanics, Science & Technology Other Topics.





You can send your paper any format in the first version (Your Paper Your Way). If your paper is accepted, you must provide the items required for the publication of your article. The Paper Template (Latex files) can be downloaded from the following link,

Paper Template: chta_template

When submitting a paper, the corresponding author should check that he or she has the right to publish it and that it does not contain any defamatory material. The CHTA will assume that all co-authors have agreed to the paper's submission.

The journal publishes previously unpublished manuscripts that will have a high impact in the field of chaos theory and applications in applied sciences and engineering. It targets not only certain field specialists but the wider public also. Papers should be submitted in Microsoft Word (*.doc, *.docx), tex or pdf format.

Abstract: It should not exceed 300 words.

Keywords: It should start with a bold “Keywords” title and should not exceed six keywords.

Introduction: For the introduction, authors should be mindful of the broad readership of the journal. The introduction should set the stage for the importance of the work to a generalist reader and draw the reader into the specific study. The scope and impact of the work should be clearly stated.

Co-Authorship: Place the author's name, affiliation and full address under the title. The affiliation and full addresses of each co-author must be specified in the case of multiple authorship of a submitted article. If more than one writer is present, please indicate clearly with an asterisk(*) who will handle the correspondence at all levels of refereeing and publishing, including post-publishing. Any alteration in the author names listed in the original manuscript, including additions, deletions, and/or changes in appearance order, requires proof of consent from all co-authors. When the paper is approved, it is forbidden to further switch co-authors.

Conflicts of Interest: Authors should state whether or not they have a financial relationship with the sponsoring entity. This note should be added to the reference list in an unnumbered separate section. If no conflict exists, authors should state: The authors declare that there is no conflict of interest regarding the publication of this paper.

Ethics: The originality of the manuscript submitted is the responsibility of the publisher. Submission, plagiarism, and self-plagiarism must be avoided by writers. Manuscript submission in the CrossCheck server (http:/www.ithenticate.com/) will be checked for plagiarism. iThenticate is a system that tests the originality of the submitted material and helps detect plagiarism. Authors can also use iThenticate to display their own credentials prior to submission.

Permissions: Authors wishing to include statistics, tables or text passages that have already been published elsewhere are required to obtain permission from the copyright owner(s) for both the print and online formats and to include proof that such permission was granted when submitting their articles. Any material received without such evidence will be assumed to originate from the authors.

Paper and Text Format: The document should be written using the Latex template that can be downloaded from the Templates. Use the styles specified in this document to edit all text. Manuscripts must be written in English and correct grammar and punctuation, in 12-point type, double spaced throughout, including the Literature Cited section and appendices, marked with consecutive page numbers, beginning with the cover page contain sections in the order shown below (Abstract, Introduction, Materials and Methods, Results and Discussion).

Tables, Figures and Images: For the review process, tables can be embedded in the manuscript or submitted as separate files. Avoid shading, colour type, line drawings, graphics, or other illustrations within tables. Use tables for data only; present drawings, graphics, and illustrations as separate figures. Histograms should not be used to present data that can be captured easily in text or small tables, as they take up much more space. Tables should be in the LaTeX file.

Figures must be followed by an accompanying caption. Links to text tables are not abbreviated, e.g. "in Table I." If your figure has two or more parts, include the "(a)" and "(b)" labels after each part as separate text, etc. Figure axis labels are often a source of confusion. Use words rather than symbols. Figure labels, roughly 8 to 11-point size, should be legible. Make sure the artwork includes the axis labels and other items. It is necessary to mention all the figures and tables in the document.

Image quality is very critical for the replication of your graphics. While graphics can be accepted in many formats, if they are of poor quality, we won't be able to upgrade your graphics. All files must conform to these resolution ranges: Halftone (colour or black & white): 200-300 dpi, Grayscale and colour combination images: 300-500 dpi. Please note that the journal publishes colour figures in the online versions and black and white figures in print. All figures without colour should be understandable. Each file must be no larger than 10 MB; figures should be 10-20 cm in width and 1-25 cm in height.

Equations: To accurately represent the math characters in your article, please use MathType 5.0 or later for equations that need math characters not found on your keyboard. Consecutive numbers with the right margin should be labelled in flush parentheses as in (1). All symbols in the equation must be defined before the equation appears or immediately following.

Abbreviations and Acronyms: Avoid abbreviations or abstract acronyms unless they are commonly understood and used in the abstract multiple times. If the article uses an abbreviation or acronym, it must be spelt out (defined) in the abstract, and then spelt out the first time it is used in the paper's main text.

References: For initial submission and review, you may submit manuscripts with references formatted in the style of another journal. However, if your manuscript is accepted for publication, please format the references as they appear in a recent article of CHTA (in the style of APA).


Discussion and Conclusions: Discussion may present insights and interpretation of the research results. It is needed to be told what the results mean. Conclusions that state your paper's most important result, not repeat the abstract as the conclusion. Conclusions may expand on the paper's relevance or propose implementations and extensions at a lower abstraction level than the discussion.
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Academic impartiality and scientific quality are important criteria in the evaluation of articles submitted for publication. Therefore, the recommendations of the ICMJE (International Committee of Medical Journal Editors) and the International Standards for Editors and Authors of COPE (Committee on Publication Ethics) should be taken into account in scientific articles submitted to the CHTA journal.

Other General Information for Authors

• CHTA is an international peer-reviewed journal that publishes high-quality articles on chaos theory and applications.
• CHTA issues were published regularly at the end of each following month: No. 1 - June, No. 2 - November (2019-2021). They will be published three times (30th of March, July, and November) for each year after 2021.
• The language of the articles is English.
• The percentage of similarity in articles should be less than 25% without references.
• Paper submissions are not accepted via e-mail.
• Ethics committee approval must be obtained for all studies on clinical and experimental humans and animals.
• Manuscripts to be published must be sent via the "Submit a Manuscript" page. 

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Submission Checklist

The following submission checklist will appear on the article submission screen (7 items). Please read these items carefully, approve them and submit your paper to the journal.

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Price Policy

All papers in Chaos Theory and Applications (CHTA) are published under Open Access. To provide readers with free access and to cover the costs of peer review, copyediting, typesetting, promotion, technical support, and journal management, to manage the various minimum costs associated with handling and editing the submitted manuscripts, an article processing charge (APC) of USD $550 (which is not refundable) is applied to any paper submitted after February 21st, 2024.

Once an article is accepted, the corresponding author will be notified that payment is due, and need to arrange the payment promptly. Instructions for fee transfer will be provided by the journal team with the notification of acceptance for the accepted papers.

50% discount is applied for authors who have served as reviewers in Chaos Theory and Applications journal in the last year. 

Article Processing Charges (APCs): 550.00 USD
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✔ Copyright Agreement

This paper (including the text, tables, figures, graphs, images, and any other related content) has not been published in the same form elsewhere.
It will not be submitted anywhere else for publication prior to acceptance/rejection by this journal.
If the manuscript has been published in whole or in part, all permissions were granted for publication in Chaos Theory and Applications (CHTA).
The paper does not include any copyright material, or all required permissions have been obtained.
Authors must ensure that their paper meets the requirements mentioned in the ethical standards of CHTA that can be viewed at https://dergipark.org.tr/en/pub/chaos/policy. Authors are advised especially of "Ethical Responsibilities of Authors" section of the ethical standards of CHTA.
The corresponding author accepts responsibility for releasing this material on behalf of any and all co-authors. Responsibility for the content of published papers rests upon the authors, not CHTA.
By confirming this item, authors agree that the paper, if accepted for publication by the Chaos Theory and Applications (CHTA), will be licensed under a Creative Commons Attribution-Non Commercial 4.0 International License (CC BY-NC) which allows third parties to share and adapt the material for only non-commercial purposes by giving the appropriate credit to the original work. For further details of the license CC BY-NC 4.0, please see https://creativecommons.org/licenses/by-nc/4.0/.
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✔ Ethical Considerations

In the event of argued or suspected research misconduct, e.g., plagiarism, citation manipulation, and data falsification/fabrication, the Editorial Board will follow and act according to COPE flowcharts.
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✔ Declaration of Interest Statement

The authors declare that none of their known financial conflicts of interest or closely associated personal relationships might have appeared to have influenced the research presented in this paper.
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✔ Plagiarism

Notice that our journal applies very strict parameters of text novelty, in order to avoid possible problems of plagiarism and self-plagiarism. Texts with overlaps larger than 25% are not considered.
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✔ Writing Rules

You can send your paper any format in the first version (Your Paper Your Way). If your paper is accepted, you must provide the items required for the publication of your article. The Paper Template (Latex files) can be downloaded from the following link,

Paper Template: chta_template

When submitting a paper, the corresponding author should check that he or she has the right to publish it and that it does not contain any defamatory material. The CHTA will assume that all co-authors have agreed to the paper's submission.

For more: https://dergipark.org.tr/en/pub/chaos/writing-rules
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✔ ORCID Numbers

I know that the ORCID numbers and email addresses of "all" authors are mandatory, and they are provided in the manuscript (visit https://orcid.org for more details on ORCID).
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Publication Ethics

The publication process at Chaos Theory and Applications is the basis of the improvement and dissemination of information objectively and respectfully. Therefore, the procedures in this process improves the quality of the studies. Peer-reviewed studies are the ones that support and materialize the scientific method. At this point, it is of utmost importance that all parties included in the publication process (authors, readers and researchers, publisher, reviewers and editors) comply with the standards of ethical considerations. Chaos Theory and Applications expects all parties to hold the following ethical responsibilities.

The following ethical duties and responsibilities are written in the light of the guide and policies made by Committee on Publication Ethics (COPE).

Ethical Responsibilities of Authors

The authors who submit their manuscripts to Chaos Theory and Applications are expected to comply with the following ethical responsibilities:
  • Author(s) must submit original studies to the journal. If they utilize or use other studies, they must make the in-text and end-text references accurately and completely.
  • People who have not contributed to the study at the intellectual level should not be indicated as author.
  • If the manuscripts submitted to be published are subject of conflicting interests or relations, these must be explained.
  • During the review process of their manuscripts, author(s) may be asked to supply raw data. In such a case, author(s) should be ready to submit such data and information to the editorial and scientific boards.
  • Author(s) should document that they have the participants' consent and the necessary permissions related with the sharing and research/analysis of the data that are used.
  • Author(s) bears the responsibility to inform the editor of the journal or publisher if they happen to notice a mistake in their study which is in early release or publication process and to cooperate with the editors during the correction or withdrawal process.
  • Authors cannot submit their studies to multiple journals simultaneously. Each submission can be made only after the previous one is completed. A study published in another journal cannot be submitted to Chaos Theory and Applications. Author responsibilities given in a study (e.g.: adding an author, reordering of author names) whose review process has begun cannot be changed.

Ethical Responsibilities of Editors

The editor and field editors of Chaos Theory and Applications should hold the following ethical responsibilities that are based on the guides "COPE Code of Conduct and Best Practice Guidelines for Journal Editors" and "COPE Best Practice Guidelines for Journal Editors" published as open Access by Committee on Publication Ethics (COPE).

General duties and responsibilities

Editors are responsible for each study published in CHTA. In this respect, the editors have the following roles and responsibilities:
  • Making efforts to meet the demand for knowledge from readers and authors
  • Ensuring the continuous development of the journal,
  • Managing the procedures aimed to improve the quality of the studies published in the journal,
  • Supporting freedom of expression,
  • Ensuring academic integrity,
  • Following the procedures without making concessions on intellectual property rights and ethical standards,
  • Being transparent and clear in issues that require correction or explanation.

Relationships with Readers

Editors must make decisions taking into consideration the knowledge, skills and expectations of all readers, researchers and practitioners need. They must also ensure that the published studies contribute to literature and be original. Moreover, they must take notice of the feedback received from researchers and practitioners and provide explanatory and informative feedback.

Relationships with Authors

Editors have the following duties and responsibilities in their relations with authors:

  • Editors must make positive or negative decisions about the studies' importance, originality, validity, clarity in wording and suitability with the journal's aims and objectives.
  • Editors must accept the studies that are within the scope of publication into pre review process unless there are serious problems with the study.
  • Editors must not ignore positive suggestions made by reviewers unless there are serious problems with the study.
  • New editors, unless there are serious issues, must not change the previous editor's decisions about the studies.
  • "Blind Review and Review Process" must be published and editors must prevent possible diversions in the defined processes.
  • Authors should be provided with explanatory and informative feedback.

Relationships with Reviewers

Editors have the following duties and responsibilities in their relations with reviewers:

Editors must

  • Choose reviewers according to the subject of the study.
  • Provide the information and guidance reviewers may need during the review process.
  • Observe whether there are conflicting interests between reviewers and authors.
  • Keep the identities of reviewers confidential in blind review.
  • Encourage the reviewers to review the manuscript in an unbiased, scientific and objective tone.
  • Develop practices and policies that increase the performance of reviewers.
  • Take necessary steps to update the reviewer pool dynamically.
  • Prevent unkind and unscientific reviews.
  • Make effort to ensure the reviewer pool has a wide range.

Relationships with the Editorial Board

Editors must make sure that the members of the editorial board follow the procedures in accordance with the publication policies and guidelines, and must inform the members about the publication policies and developments. Moreover, editors must

  • Ensure that the members of the editorial board review the manuscripts in an unbiased and independent manner.
  • Select the new members of the editorial board from those who can contribute to the journal and are qualified enough.
  • Send manuscripts for review based on the subject of expertise of the editorial board members.
  • Regularly communicate with the editorial board.Arrange regular meetings with the editorial board for the development of publication policies and the journal.

Relationships with the Journal's Owner and Publisher

The relationship between the editors and publisher is based on the principle of the independency of editors. All the decisions made by the editors are independent of the publisher and the owner of the journal as required by the agreement made between editors and publisher.

Editorial and Blind Review Processes

Editors are obliged to comply with the policies of "Blind Review and Review Process" stated in the journal's publication policies. Therefore, the editors ensure that each manuscript is reviewed in an unbiased, fair and timely manner.

Quality Assurance

Editors must make sure that articles in the journal are published in accordance with the publication policies of the journal and international standards.

Protection of Personal Information

Editors are supposed to protect the personal information related with the subjects or visuals in the studies being reviewed, and to reject the study if there is no documentation of the subjects' consent. Furthermore, editors are supposed to protect the personal information of the authors, reviewers and readers.

Encouraging Ethical Rules and Protection of Human, Animal or Hazards Rights

Editors are supposed to protect human and animal rights in the studies being reviewed and must reject the experimental studies which do not have ethical and related committee’s approval about the population given in such studies.

Editors will review the submitted manuscripts on animal well-being issues, and the manuscript is likely to be rejected if the research is deemed to violate accepted standards for employing both animal and human subjects. Additionally, Editors retain the right to get in touch with the approving committee for any additional explanation. All experiments involving animals must adhere to the ARRIVE guidelines.

Please be aware that researchers have a moral responsibility to treat humans and animals with compassion and to take into account their needs when planning projects. This obligation extends to both animal and human subjects. In addition, the author must clearly identify in the paper any exceptional hazards associated with the use of any chemicals, methods, or equipment used in the work.

The author should make sure the paper contains a statement that all procedures were carried out according to with applicable laws and institutional policies and that the appropriate institutional committee(s) have approved them if the work involves the use of human or animal subjects. Informed consent for experiments involving human participants should be given by the authors in their paper. Human subjects' privacy must always be respected. The Code of Ethics of the World Medical Association (Declaration of Helsinki) for research involving humans should have been followed, as stated by the author, when using human subjects.

Precautions against possible Abuse and Malpractice

Editors are supposed to take precautions against possible abuse and malpractice. They must conduct investigations meticulously and objectively in determining and evaluating complaints about such situations. They must also share the results of the investigation.

Ensuring Academic Integrity

Editors must make sure that the mistakes, inconsistencies or misdirections in studies are corrected quickly.

Protection of Intellectual Property Rights

Editors are responsible for protecting the intellectual property rights of all the articles published in the journal and the rights of the journal and author(s) in cases where these rights are violated. Also, editors must take the necessary precautions in order to prevent the content of all published articles from violating the intellectual property rights of other publications.

Constructiveness and Openness to Discussion

Editors must

  • Pay attention to the convincing criticism about studies published in the journal and must have a constructive attitude towards such criticism.
  • Grant the right of reply to the author(s) of the criticized study.
  • Not ignore or exclude the study that include negative results.

Complaints

Editors must examine the complaints from authors, reviewers or readers and respond to them in an explanatory and enlightening manner.

Political and Economic Apprehensions

Neither the owner of the journal, publisher or any other political or economical factor can influence the independent decision taking of the editors.

Conflicting Interests

Editors, acknowledging that there may be conflicting interests between reviewers and other editors, guarantee that the publication process of the manuscripts will be completed in an independent and unbiased manner.

Ethical Responsibilities of Reviewers

The fact that all manuscripts are reviewed through "Blind Review" has a direct influence on the publication quality. This process ensures confidentiality by objective and independent review. The review process at CHTA is carried out on the principle of double blind review. Reviewers do not contact the authors directly, and the reviews and comments are conveyed through the journal management system. In this process, the reviewer views on the evaluation forms and full texts are assigned to the author(s) by the editor. Therefore, the reviewers doing review work for CHTA are supposed to bear the following ethical responsibilities:

Reviewers must

  • Agree to review only in their subject of expertise.
  • Review in an unbiased and confidential manner.
  • Inform the editor of the journal if they think that they encounter conflict of interests and decline to review the manuscript during the review process.
  • Dispose the manuscripts they have reviewed in accordance with the principle of confidentiality after the review process. Reviewers can use the final versions of the manuscripts they have reviewed only after publication.
  • Review the manuscript objectively and only in terms of its content and ensure that nationality, gender, religious and political beliefs, and economic apprehension do not influence the review.
  • Review the manuscript in a constructive and kind tone, avoid making personal comments including hostility, slander and insult.
  • Review the manuscript they have agreed to review on time and in accordance with the ethical rules stated above.

Please see also the Peer-Review Process and Guide for Reviewers.

Ethical Responsibilities of Publisher

The Editors and the Editorial Board of CHTA are conscious of the fact that they must observe the ethical responsibilities below and act accordingly:

  • Editors are responsible for all the processes that the manuscripts submitted to CHTA will go through. Within this framework, ignoring the economic or political interests, the decision-makers are the editors.
  • The publisher undertakes to have an independent editorial decision made.
  • The originality of the manuscript submitted is the responsibility of the publisher. Submission, plagiarism, and self-plagiarism must be avoided by writers. Manuscript submission in the CrossCheck server (http:/www.ithenticate.com/) will be checked for plagiarism. iThenticate is a system that tests the originality of the submitted material and helps detect plagiarism. Authors can also use iThenticate to display their own credentials prior to submission. 
  • The publisher protects the intellectual property rights of all the articles published in CHTA and holds the responsibility to keep a record of each unpublished article.
  • The publisher bears all the responsibility to take the precautions against scientific abuse, fraud and plagiarism.

Unethical Behaviour

Should you encounter any unethical act or content in CHTA apart from the ethical responsibilities listed above, please notify the journal by e-mail at journalofchta@gmail.com.

All papers in Chaos Theory and Applications (CHTA) are published under Open Access. To provide readers with free access and to cover the costs of peer review, copyediting, typesetting, promotion, technical support, and journal management, to manage the various minimum costs associated with handling and editing the submitted manuscripts, an article processing charge (APC) of USD $550 (which is not refundable) is applied to any paper submitted after February 21st, 2024.

Once an article is accepted, the corresponding author will be notified that payment is due, and need to arrange the payment promptly. Instructions for fee transfer will be provided by the journal team with the notification of acceptance for the accepted papers.

50% discount is applied for authors who have served as reviewers in Chaos Theory and Applications journal in the last year.

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Payment Instructions
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* Payment by Bank Transfer
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Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830 28903   

The published articles in CHTA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License Cc_by-nc_icon.svg