Calcium is essential for various physiological processes in the human body, including the regulation of heartbeats, muscle contractions, bone metabolism, and brain function. Multiple researchers have conducted studies on calcium signaling in neuron cells in order to acquire a more comprehensive understanding of its mechanics. However, very limited research has concentrated on examining the interdependence underlying calcium signaling and IP \(_3\) signaling in neuronal cells. The structure of the present model delves into the nonlinear behavior of interdependent dynamical systems of calcium and IP \(_3\) signaling within neuronal cells. The numerical findings were obtained using the Crank-Nicholson approach in conjunction with a finite difference scheme. The Gauss-Seidel method has been employed to solve the resulting nonlinear reaction-diffusion equations. The current study focuses on a nonlinear mathematical model that examines the functions of several crucial mechanisms of calcium and IP \(_3\) signaling and their significant impacts on the dynamical systems of \([\text {Ca}^{2+}]\) and IP \(_3\) in neuron cells. Also, the present work provides insights into the functioning of different crucial mechanisms, which significantly differ for individual systems of calcium and interdependent systems of calcium and IP \(_3\) in neurons. The alterations in any mechanism of calcium and IP \(_3\) signaling may cause dysregulation in interdependent dynamical systems of \([\text {Ca}^{2+}]\) and IP \(_3\) in neurons and are responsible for different neurological illnesses, such as Alzheimer’s disease (AD).