Nonlinear Dynamics, Chaos and Complex Systems
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".
Deadline for manuscript submissions: 30 November 2024 | Viewed by 155
Special Issue Editor
Special Issue Information
Dear Colleagues,
Talking about dynamics is often challenging because it has gained importance in understanding natural phenomena through differential equations proposed by Newton and Leibniz at the start of the 17th century.
Following these seminal works, several fields of natural sciences developed models and ways to describe their study objects by considering how the various observable variables evolve depending on temporal and spatial dynamics.
Starting with ordinary equations for mechanical problems, the idea was to provide exact analytical solutions that, until now, are difficult to obtain in a general fashion.
Considering the broader development of engineering and physics during the 18th and 19th centuries, continuous fluid mechanics and electromagnetism were characterized by partial derivative equations with rigorous mathematical formulations, proposed by Navier, Stokes, and Maxwell.
At the start of the 20th century, Poincaré formulated the three-bodies problem, wherein initial proximity of the bodies could lead to divergence due to nonlinearities.
Connecting this idea with the turbulence phenomenon, Ruelle and Takens proposed that nonlinearities and high state space dimensions would be responsible for this intriguing nature manifestation.
Nowadays, chaos, initial condition sensitivity, noise due to nonlinearities, unpredictability, and complexity appear in all science studies: meteorology, physics, engineering, chemistry, biology, and social sciences; nonlinear dynamics is ubiquitous.
This Special Issue welcomes the inclusion of various approaches and study areas, which have been thoroughly examined and discussed.
Prof. Dr. José Roberto Castilho Piqueira
Guest Editor
Manuscript Submission Information
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Keywords
- bifurcations
- center manifolds
- chaotic behaviors
- dynamical models
- nonlinear oscillations
