•A new chaotic system with infinitely many coexisting attractors is presented. The dynamic behaviors of the new system are studied. The abundant coexisting attractors of the system are presented.•The electronic circuit and microcontroller-based implementation of the new system is studied. The consistence between the circuit outputs and the simulation results physically illustrates the existence of the system.•The synchronization problem of the new system is studied by using the sliding mode control method and the corresponding synchronization conditions are established. This paper reports a new chaotic system generated from the simplest memristor chaotic circuit by introducing a simple nonlinear feedback control input. The principal feature of the new system is that it has infinitely many equilibria and abundant coexisting attractors. The dynamic evolution of the system with respect to parameters and initial conditions is given to illustrate the existence of chaos and coexisting attractors. The circuit implementation is done for demonstrating the physical existence of the system. A microcontroller on Arduino Mega 2650 board is used to realize the system. Also the synchronization problem of the system is analyzed with the establishment of synchronization conditions based on the sliding mode control.