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A large number of biological systems - from bacteria to sheep - can bedescribed as ensembles of self-propelled agents (active particles) with acomplex internal dynamic that controls the agent's behavior: resting, movingslow, moving fast, feeding, etc. In this study, we assume that such a complexinternal dynamic can be described by a Markov chain, which controls the movingdirection, speed, and internal state of the agent. We refer to this Markovchain as the Navigation Control System (NCS). Furthermore, we model that agentssense the environment by considering that the transition rates of the NCSdepend on local (scalar) measurement of the environment such as e.g. chemicalconcentrations, light intensity, or temperature. Here, we investigate underwhich conditions the (asymptotic) behavior of the agents can be reduced to aneffective convection-diffusion equation for the density of the agents,providing effective expressions for the drift and diffusion terms. We apply thedeveloped generic framework to a series of specific examples to show that inorder to obtain a drift term two conditions should be fulfilled: i) the NCStransition rates should depend on the agent's position, and ii) transitionrates should be asymmetric. In addition, we indicate that the sign of the driftterm - i.e. whether agents develop a positive or negative chemotactic response- can be changed by modifying the asymmetry of the NCS or by swapping the speedassociated to the internal states. The developed theoretical framework pavesthe way to model a large variety of biological systems and provides a solidproof that chemotactic responses can be developed, counterintuitively, byagents that cannot measure gradients and lack memory as to store pastmeasurements of the environment.

Kinetic and macroscopic models for active particles exploring complex environments with an internal navigation control system