<p>Discrete dynamical models have been proposed in neural systems. Given that the neural cells have complex dendrites and relatively simple axons, the equivalent circuit inspired by the voltage-gated ion channels with nonlinear effects is reconstructed. Here, we utilize two capacitors to characterize the bioinspired bi-membrane effect. The interactions between two membranes are complex and different. Thus, the quadratic nonlinear currents are employed to describe the bi-membrane mutual effects. Considering the complex dendritic structure, the nonlinear ionic currents are replaced by the equivalent memristive Josephson currents. In terms of the time scale, the discrete bi-membrane neuron-like model can exhibit abundant dynamical behaviors through a bifurcation mechanism, and the corresponding result is demonstrated by using numerical simulation. From the spatiotemporal point of view, we successfully replicate the characteristic spiral waves and can destroy regular waves when the memristive or Josephson current is activated. Finally, a new image encryption algorithm is proposed by blinding with the discrete model from the time and space effect. The obtained results point out that the new algorithm can achieve more efficient image encryption.</p>