The mimicking of classical conditioning, including acquisition, extinction, recovery, and generalization, can be efficiently achieved by using a single flexible memristor. In particular, the experiment of Pavlov's dog is successfully demonstrated. This demonstration paves the way for reproducing advanced neural processes and provides a frontier approach to the design of artificial-intelligence systems with dramatically reduced complexity.

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In this paper, we consider the nonlinear Kirchhoff-type equation $$ u_{tt} + M(\left\| {D^m u(t)} \right\|_2^2 )( - \Delta )^m u + \left| {u_t } \right|^{q - 2} u_t = \left| {u_t } \right|^{p - 2} u $$ with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time.

This paper is concerned with the nonlinear full Marguerre-von Kármán shallow shell system with a dissipative mechanism of memory type. The model depends on one small parameter. The main purpose of this paper is to show that as the parameter approaches zero, the limiting system is the well-known full von Kármán model with memory for thin plates.