A mathematical model of the mammalian ventricular cardiac action potential is introduced, incorporating recent single-cell and single-channel data, and considering changes in extracellular potassium concentration. The model includes a fast sodium current (I_Na) with a high upstroke velocity and slow recovery from inactivation, and a time-independent potassium current (I_K1) with a negative-slope phase and significant crossover behavior. A novel potassium current (I_Kp) that activates at plateau potentials is also included. The model accurately simulates the effects of extracellular potassium concentration on action potential duration and resting potential. The model's simulations focus on the interaction between depolarization and repolarization, showing the importance of the slow recovery of I_Na in determining cell response. Simulations of periodic stimulation reveal different patterns, including Wenckebach periodicity and alternans at normal potassium concentrations, while at low concentrations, nonmonotonic Wenckebach patterns, aperiodic responses, and enhanced supernormal excitability (chaotic activity) are observed. These results align with experimental observations and relate phenomena to ionic channel kinetics. The model is based on the Hodgkin-Huxley formalism and uses numerical methods to solve differential equations. It incorporates parameters derived from experimental data and includes detailed formulations for ionic currents. The model's simulations demonstrate the effects of extracellular potassium concentration on action potential characteristics, including changes in resting potential and action potential duration. The model also investigates the role of sodium channel recovery in determining membrane excitability and the mechanisms underlying supernormal excitability. The model's simulations show that the slow recovery of the sodium channel is crucial for the observed phenomena, and that the shape of the threshold potential curve is determined by the recovery of the sodium channel. The model's results provide insights into the mechanisms of cardiac electrophysiology and the effects of extracellular potassium concentration on cardiac function.A mathematical model of the mammalian ventricular cardiac action potential is introduced, incorporating recent single-cell and single-channel data, and considering changes in extracellular potassium concentration. The model includes a fast sodium current (I_Na) with a high upstroke velocity and slow recovery from inactivation, and a time-independent potassium current (I_K1) with a negative-slope phase and significant crossover behavior. A novel potassium current (I_Kp) that activates at plateau potentials is also included. The model accurately simulates the effects of extracellular potassium concentration on action potential duration and resting potential. The model's simulations focus on the interaction between depolarization and repolarization, showing the importance of the slow recovery of I_Na in determining cell response. Simulations of periodic stimulation reveal different patterns, including Wenckebach periodicity and alternans at normal potassium concentrations, while at low concentrations, nonmonotonic Wenckebach patterns, aperiodic responses, and enhanced supernormal excitability (chaotic activity) are observed. These results align with experimental observations and relate phenomena to ionic channel kinetics. The model is based on the Hodgkin-Huxley formalism and uses numerical methods to solve differential equations. It incorporates parameters derived from experimental data and includes detailed formulations for ionic currents. The model's simulations demonstrate the effects of extracellular potassium concentration on action potential characteristics, including changes in resting potential and action potential duration. The model also investigates the role of sodium channel recovery in determining membrane excitability and the mechanisms underlying supernormal excitability. The model's simulations show that the slow recovery of the sodium channel is crucial for the observed phenomena, and that the shape of the threshold potential curve is determined by the recovery of the sodium channel. The model's results provide insights into the mechanisms of cardiac electrophysiology and the effects of extracellular potassium concentration on cardiac function.