Dimension estimate of the exponential attractor for the chemotaxis-growth system

We consider a chemotaxis-growth model which takes into account diffusion, chemotaxis, production of chemical substance, and growth. We present estimates from above and below of the fractal dimension dim R of the exponential attractor R in terms of the coefficients of the system. Comparisons are made between the sizes of the global and exponential attractors. Numerical simulations are presented which confirm the analytical results obtained.