Nonlinear space-time dynamics, defined in terms of celebrated 'solitonic' equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. In this paper, we review sine–Gordon solitons, kinks and breathers as models of nonlinear excitations in complex systems in physics and in living… (More)
This paper proposes a novel chaotic reaction-diffusion model of cellular tumor growth and metastasis. The model is based on the multiscale diffusion cancer-invasion model (MDCM) and formulated by introducing strong nonlin-ear coupling into the MDCM. The new model exhibits temporal chaotic behavior (which resembles the classical Lorenz strange attractor) and… (More)
These lecture notes in Lie Groups are designed for a 1–semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engineering and biomechanics. We give both… (More)
DNA molecule is a complex dynamical system consisting of many atoms having a quasi-one-dimensional structure. In this paper, we first review non-linear Hamiltonian DNA dynamics in the form of several Peyrard-Bishop-type DNA models. Then, we explore Hamiltonian chaos and thermodynamical phase transitions related to Hamiltonian DNA dynamics. These… (More)
This paper proposes rigorous geometrical treatment of bioelectrodynamics, underpinning two fast–growing biomedical research fields: bioelectromagnetism, which deals with the ability of life to produce its own electromagnetism, and bioelectromagnetics, which deals with the effect on life from external electromagnetism.