Associate Professor · INFI/UFMS

Marcus Varanis

Modeling complex systems beyond linearity and stationarity.

I am an associate professor at the Institute of Physics (INFI/UFMS) and lead the Nonlinear Dynamics and Signal Processing Group. My work combines analytical modeling, computational experiments, advanced signal analysis, and scientific machine learning to investigate nonlinear mechanical and biomedical systems.

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ẍ + δẋ + αx + βx³ = γ cos(ωt)

Group Leader

Marcus Varanis

01 — About

A physicist working at the intersection of theory, experiment, and computation.

I am an associate professor at the Institute of Physics (INFI), Universidade Federal de Mato Grosso do Sul (UFMS), in Campo Grande, Brazil. I earned a D.Sc. in Mechanical Engineering from the School of Mechanical Engineering at Universidade Estadual de Campinas (UNICAMP) and completed postdoctoral research in the Department of Mechanical Engineering at UNESP Bauru.

I am affiliated with the Graduate Program in Materials Science (PPGCM/INFI), where I teach undergraduate and graduate courses, advise undergraduate researchers and master's and doctoral students, and lead the Nonlinear Dynamics and Signal Processing Group.

My research and teaching encompass nonlinear dynamics and vibrations, time-frequency analysis, fractional-order systems, scientific machine learning, and biomedical modeling. Within time-frequency analysis, my work includes wavelet packet methods, the Hilbert-Huang transform, synchrosqueezing, and synchroextracting transforms.

I also maintain active collaborations with research groups in Brazil and abroad.

02 — Research

Five interlocking lines, one question.

How do real systems behave when linearity, stationarity, and isolation cease to be valid assumptions, and how can we measure, model, and predict that behavior?

Explore the full research portfolio →

Nonlinear Dynamics & Mechanical Vibrations

Nonlinear oscillators, nonideal excitation and the Sommerfeld effect, vibro-impact dynamics, synchronization, fractional-order damping and memory effects, and mechanical energy harvesting.

Nonstationary Signal Processing

Wavelet and wavelet packet analysis, synchrosqueezing and synchroextracting transforms, variational mode decomposition, and energy-entropy signatures for nonlinear and nonstationary signals.

Scientific Machine Learning

Hamiltonian and Lagrangian Neural Networks, physics-informed learning, and multimodal deep learning for reconstructing and classifying dynamical regimes, including chaotic and hyperchaotic behavior.

Computational Biomedical Modeling

Nonlinear models of chest wall mechanics and cardiopulmonary dynamics during CPR, nonlinear Windkessel hemodynamics, and coupled Van der Pol oscillators for cardiac rhythm modeling.

Teaching & Research Training

Physically grounded computational frameworks and Feynman-inspired teaching materials for nonlinear dynamics, computational modeling, and simulation, supporting undergraduate research (Iniciação Científica) and master's and doctoral training.

03 — Group

A research collective at INFI/UFMS bridging analytical theory, computational experiments and physical instrumentation. The group brings together doctoral and graduate researchers alongside undergraduate (Iniciação Científica) students, working across scientific machine learning, fractional and nonlinear dynamics, watch-mechanism modelling and energy harvesting.

PhD

João Vitor de Oliveira Ribas

PhD Candidate · PPGCM/INFI

Analysis and Modeling of Metamaterials using Hamiltonian and Lagrangian Neural Networks · SciML for dynamical systems.

Barbara Oliveira

Master's student

Coupled 0D–1D cardiovascular modelling · wave-propagation effects and nonlinear stent models

Rodrigo Carvalho

Graduate Researcher

Metamaterials Scientific Machine Learning

Mateus Silva

Graduate Researcher

Fractional-Order Systems · memory-effect dynamics

Antonio

Undergraduate

Symbolic Hamiltonian formulation

Nickolas

Undergraduate

Physics-Informed Neural Networks

Pablo

Undergraduate

Symbolic Hamiltonian formulation

Dilson

Undergraduate

Coupled 0D–1D cardiovascular modelling

Lívia

Undergraduate

Mechanical Vibrations Instrumentation

Paulo

Undergraduate

Energy Harvesting · modelling and simulation

João Dutka

Undergraduate

Numerical analysis of the dynamics of the clock mechanism.

Diogo

Undergraduate

Symbolic analysis of the dynamics of the clock mechanism.

Daniela

Undergraduate

Signal processing and time-frequency analysis of LIGO signals.

Eduardo Venturim

Undergraduate

Nonlinear flutter modelling

Open Call

Master's and undergraduate research positions are available in scientific machine learning, signal processing, and nonlinear dynamics.

Applications from Brazil and abroad are welcome.

Apply

04 — Active Projects

Living artifacts, not a list of papers.

Each project below is a real, named, ongoing piece of work — with collaborators and a roadmap.

CPR

Nonlinear Chest Wall and Cardiopulmonary Modeling for CPR

A coupled computational model of nonlinear viscoelastic chest wall mechanics and cardiopulmonary circulation during CPR.

Areas · Biomedical modeling · Nonlinear dynamics

Collaborators · Prof. C. Nataraj · Villanova Center for Analytics of Dynamic Systems (VCADS), Villanova University

PQD

Power Quality Disturbance Modeling and Classification

A signal processing and scientific machine learning framework for representing and classifying power quality disturbance signals.

Areas · Signal processing · Scientific machine learning

Methods · IEEE 1159-2019 · Wavelet packet analysis · Entropy features · FT-Transformer

Team · Nonlinear Dynamics and Signal Processing Group

SciML

Scientific Machine Learning for Nonlinear Systems

Hamiltonian and Lagrangian Neural Networks for the analysis of nonlinear dynamical systems and applications in materials science.

Scope · Research · Teaching

Methods · Neural ODEs · HNNs and LNNs · PyTorch · Google Colab

Collaborators · Prof. Américo Cunha Jr. (LNCC, Brazil) · Prof. J. M. Balthazar (UNESP, Brazil)

NLD

Nonlinear Dynamical Systems

Analytical, computational, and experimental studies of nonlinear systems in mechanics and engineering, with emphasis on oscillations, stability, bifurcations, chaos, synchronization, vibro-impact, nonideal excitation, fractional-order effects, and energy harvesting.

Areas · Nonlinear dynamics · Mechanical vibrations · Applied mechanics

Collaborators · J. M. Balthazar (UNESP, Brazil); Grzegorz Litak (Lublin University of Technology, Poland); Américo Cunha Jr. (LNCC, Brazil); Angelo Tusset (UTFPR, Brazil); Clivaldo Oliveira (UFGD, Brazil)

05 — Publications

A research programme, not a chronology.

Selected work organized by research line. First-author contributions are marked; the complete record is available through the profiles below.

Scholar Lattes ResearchGate

Journal articles

Book chapters

Conference papers

Edited / co-authored books

Nonlinear Dynamics & Mechanical Vibrations

2019

Journal

Journal of the Franklin Institute

Dynamics and control of periodic and non-periodic behavior of Duffing vibrating system with fractional damping and excited by a non-ideal motor

Varanis · Tusset · Balthazar · Litak · Oliveira · Rocha · Nabarrete · Piccirillo

2020

Journal

J. Braz. Soc. Mech. Sci. Eng.

Numerical and experimental investigation of the dynamic behavior of a cantilever beam driven by two non-ideal sources

Varanis · Mereles · Silva · Barghouthi · Balthazar · Lopes · Bavastri

2019

Journal

Latin American Journal of Solids and Structures

Modeling and experimental validation of two adjacent portal frame structures subjected to vibro-impact

Varanis · Mereles · Silva · Balthazar · Tusset · Oliveira

2024

Journal

J. Braz. Soc. Mech. Sci. Eng.

Performance analysis of a nonlinear energy harvester with subharmonic responses based on discrete Meyer wavelet filtering

Ribeiro · Varanis · Tusset · Machado · Litak · Balthazar

2022

Journal

J. Braz. Soc. Mech. Sci. Eng.

A new approach to suppressing the Sommerfeld effect in vibrating structures

Brogin · Bueno · Santos · Varanis

Nonstationary Signal Processing

2021

Journal

Brazilian Journal of Physics

A tutorial review on time-frequency analysis of non-stationary vibration signals with nonlinear dynamics applications

Varanis · Silva · Balthazar · Pederiva

2018

Journal

Journal of Vibration and Control

Remarks on the Sommerfeld effect characterization in the wavelet domain

Varanis · Balthazar · Silva · Mereles · Pederiva

2018

Journal

J. Braz. Soc. Mech. Sci. Eng.

Statements on wavelet packet energy-entropy signatures and filter influence in fault diagnosis of induction motor in non-stationary operations

Varanis · Pederiva

2021

Journal

Journal of Vibration Engineering & Technologies

A short note on synchrosqueezed transforms for resonant capture, Sommerfeld effect and nonlinear jump characterization in mechanical systems

Varanis · Silva · Balthazar · Oliveira · Tusset · Bavastri

2022

Book chapter

Springer · Mechanisms and Machine Science, vol. 116

On the use of synchrosqueezing transform for chaos and nonlinear dynamics analysis in fractional-order systems

Varanis · Oliveira · Ribeiro · Lenz · Tusset · Balthazar

Computational Biomedical Modeling

2026

Journal

Medical & Biological Engineering & Computing

A nonlinear Windkessel model for cardiovascular dynamics: variable compliance and pathological simulations

Varanis · Ferraz · Longo · Balthazar

2025

Book chapter

Springer · Mechanisms and Machine Science, vol. 142

Recurrence analysis of nonlinear ECG signals modeled with coupled Van der Pol oscillators

Varanis · Balthazar · Ribeiro · Tusset · de Oliveira · Lima · Silva

2024

Book chapter

Springer · NODYCON Proceedings, vol. 3

An overview on time-frequency effects of ECG signals using synchroextracting transform

Varanis · Hemmati · Filipus · de Abreu · Balthazar · Nataraj

2026

Journal

Brazilian Journal of Physics

Influence of a non-ideal external force on the complexity of the basins of attraction of coupled Van der Pol oscillators

Ribeiro · Silva · Balthazar · de Lima · Varanis · Tusset

2025

Journal

Journal of Vibration Testing and System Dynamics

On nonlinear and nonideal dynamics of three coupled Van der Pol oscillators applied to hemodynamics

Silva · Ribeiro · Balthazar · Lima · Goncalves · Piccirilo · Varanis · Oliveira · Tusset

Teaching & Research Training

2026

Journal · In press

European Journal of Physics

Geometry to dynamics via B⊤B assembly: a Hamiltonian-first tutorial for a 6-DOF supported cube

Ferraz · Longo · Varanis

doi:10.1088/1361-6404/ae9015

2018

Journal

J. Braz. Soc. Mech. Sci. Eng.

MEMS accelerometers for mechanical vibrations analysis: a comprehensive review with applications

Varanis · Silva · Mereles · Pederiva

2018

Journal

Revista Brasileira de Ensino de Física

On mechanical vibration analysis of a multi degree of freedom system based on Arduino and MEMS accelerometers

Varanis · Silva · Mereles

2020

Journal

Revista Brasileira de Ensino de Física

An acquisition system framework for mechanical measurements with Python, Raspberry Pi and MEMS sensors

Barbosa · Varanis · Delgado · Oliveira

2024

Journal

Revista Brasileira de Ensino de Física

Fractional dynamics: a comprehensive exploration of non-integer order systems

de Abreu · Filipus · de Oliveira · Balthazar · Ribeiro · Tusset · Varanis

Gold rule marks first-author contributions.

06 — Contact

Get in touch

I welcome inquiries from prospective graduate students and researchers interested in collaboration, as well as invitations for seminars, lectures, and academic events. Graduate supervision is available through PPGCM/INFI/UFMS.

marcus.varanis@ufms.brINFI · UFMS · Campo Grande, MS · Brazil

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ẍ + δẋ + αx + βx³ = γ cos(ωt)