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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)
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)
The motivation behind mathematically modeling the human operator is to help explain the response characteristics of the complex dynamical system including the human manual controller. In this paper, we present two approaches to human operator model-ing: classical linear control approach and modern nonlinear control approach. The latter one is formalized… (More)
This paper proposes geometric Ricci–flow as a general model for reaction–diffusion systems and dissipative solitons in mathematical biology.