Analytical Investigation of Pursuit and Evasion Games for Second-Order Parameterized Systems
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This paper considers a pursuit-evasion differential game where the dynamics of play-
ers are governed by second-order parameterized differential equations. This model substantially
generalizes the problem formulation by extending the classical inertial motion to oscillating and
exponentially unstable dynamic regimes. A family of parallel pursuit strategies (Π-strategy) for the
pursuer is constructed, and exact necessary and sufficient conditions for guaranteed capture in a
finite time interval are established alongside explicit analytical formulas for optimal capture time.
Furthermore, an explicit evasion strategy for the evader is proposed, lower bounds for the distance
between players are derived, and conditions for guaranteed evasion over an infinite time horizon
are proven. The results obtain generalize and extend classical research on se
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