The pursuit-evasion problem is widespread in nature, engineering, and societal applications. It is commonly observed in nature that predators often exhibit faster speeds than their prey but have less agile maneuverability. Over millions of years of evolution, animals have developed effective and efficient strategies for pursuit and evasion. In this paper, we provide a dynamic framework for the pursuit-evasion problem of unicycle systems, drawing inspiration from nature. First, we address the scenario with one pursuer and one evader by proposing an Alert-Turn control strategy, which consists of two efficient ingredients: a sudden turning maneuver and an alert condition for starting and maintaining the maneuver. We present and analyze the escape and capture results at two levels: a lower level of a single run and a higher level with respect to parameters’ changes. In addition, we provide a theorem with sufficient conditions for capture. The Alert-Turn strategy is then extended to more complex scenarios involving multiple pursuers and evaders by integrating aggregation control laws and a target-changing mechanism. By adjusting a ‘selfish parameter’, the aggregation control commands produce various escape patterns of evaders: cooperative mode, selfish mode, and their combinations. The influence of the selfish parameter is quantified, and the target-changing mechanism is explored from a statistical perspective. Our findings align closely with observations in nature. Finally, the proposed strategies are validated through numerical simulations that replicate some chasing behaviors of animals in nature.