Global Solvability and Stability of an Alarm-Taxis System

.This paper is concerned with the global boundedness and stability of classical solutions to an alarm-taxis system describing the burglar alarm hypothesis as an important mechanism of antipredation behavior when prey species are threatened by predators. Compared to the existing prey-taxis systems, the alarm-taxis system has more complicated coupling structure and additionally requires the gradient estimate of the primary predator density to attain the global boundedness of solutions. By the sophisticated coupling energy estimates based on the Neumann semigroup smoothing properties, we establish the existence of globally bounded solutions in two dimensions with Neumann boundary conditions and furthermore prove the global stability of coexistence homogeneous steady states under certain conditions on the system parameters.Keywordsalarm-taxisglobal boundednessglobal stabilitycoexistence steady statesMSC codes35A0135B4035B4435K5735Q9292C17