Electronic circuit and image encryption for a new 3D nonuniformly conservative system

Introducing dynamical systems that involve a variable in the trace of the Jacobian matrix is a difficult challenge due to it is difficult to determine whether a system is dissipative or conservative. This paper introduces a new 3D chaotic nonuniformly conservative system with a variable in the trace of the Jacobian matrix through the Hamiltonian form. The proposed system is without equilibrium points (hidden attractors) and satisfies categories C and D. The system exhibits three distinct behaviors (chaotic, quasi-periodic, periodic) under the same parameters with varying initial conditions. The characteristics system are investigated through a combination of theoretical analysis and numerical simulations, including dissipative and conservative behavior, equilibrium points, bifurcation diagrams, Lyapunov exponents, and multistability. Finally, two applications are implemented: an electronic circuit and image encryption based on the proposed system. These outcomes substantiate the sufficiency and viability of this system, demonstrating its effective performance.