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Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
Many biological, physical, and social interactions have a particular dependence on where they take place. In living cells, protein movement between the nucleus and cytoplasm affects cellular response (i.e., proteins must be present in the…
Oscillations represent a ubiquitous phenomenon in biological systems. The conventional models of biological periodic oscillations are usually proposed as interconnecting transcriptional feedback loops. Some specific proteins function as…
This research focuses on the interesting physical phenomenon of the bead-hoop system. The bifurcation can be observed investigating the equilibrium point of the bead, and nonlinear oscillation also occurs from the bead's motion. This paper…
The work reported here aims to address the effects of time-dependent parameters and stochasticity on decision-making in biological systems. We achieve this by extending previous studies that resorted to simple normal forms. Yet, we focus…
We consider an opinion dynamics model coupled with an environmental dynamics. Based on a forward invariance argument, we can simplify the analysis of the asymptotic behavior to the case when all the opinions in the social network are…
A dynamic model for cell differentiation is studied, where cells with internal chemical reaction dynamics interact with each other and replicate. It leads to spontaneous differentiation of cells and determination, as is discussed in the…
A study is reported of the quantum scattering resonances of dissociating molecules using a semiclassical approach based on periodic-orbit theory. The dynamics takes place on a potential energy surface with an energy barrier separating two…
We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…
In various biological systems information from many noisy molecular receptors must be integrated into a collective response. A striking example is the thermal imaging organ of pit vipers. Single nerve fibers in the organ reliably respond to…
A novel theory for cell differentiation is proposed, based on simulations with interacting artificial cells which have metabolic networks within, and divide into two when the final product is accumulated. Results of simulations with coupled…
Many organic chemical reactions are governed by potential energy surfaces that have a region with the topographical features of a caldera. If the caldera has a symmetry then trajectories transiting the caldera region are observed to exhibit…
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…
Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least…
We propose and analyze a nonlinear dynamic model of continuous-time multi-dimensional belief formation over signed social networks. Our model accounts for the effects of a structured belief system, self-appraisal, internal biases, and…
We study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian;…
In this work we consider a collective decision-making process in a network of agents described by a nonlinear interconnected dynamical model with sigmoidal nonlinearities and signed interaction graph. The decisions are encoded in the…
Decision making is a fundamental capability of autonomous systems. As decision making is a process which happens over time, it can be well modeled by dynamical systems. Often, decisions are made on the basis of perceived values of the…
The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular…