How to continuously vary inductance in the range \$[-A, A]\$, A>0?
[OP:] The equations that I get for the circuits the similar to Hamiltonian of graphene. Here, the inductances and capacitances act like some parameters in the Hamiltonian and I want to vary these parameters to see how the behavior of the system changes.

It appears that you are trying to simulate &quot;the behavior of the system&quot;. Excluding the possibility that, in order &quot;to model some properties of graphene&quot;, you have chosen to build an analog computer, the insertion of lumped circuit elements into the field models of solvers for the integrated EM/materials engineering problems is a well-established approach because of the topological similarities between the finite difference scheme and circuits.
But, to begin with, you have to make sure: for the specific physical properties of the material and the environment (temperature, external fields) that you are going to study (&quot;an effective -ve value in the equations&quot;, what is it?), the quantum effects do not prevail and the purely classical-electromagnetic &quot;Hamiltonian&quot; is a reasonable approximation.
Then, you start with the generation of equivalent circuits for your problem (circuit extraction) -- the circuits that include resistors, inductors, capacitors, and voltage/current controlled voltage/current sources. The resulting elements may have non-physical values (negative inductances, for example) for some cells or even everywhere. The netlists for extracted circuits are fed into a circuit simulator (specifically, you can use SPICE), and you can expect to obtain the solution. To plot the dependence of the solutions on &quot;inductances and capacitances&quot; (if this is the right way to investigate your system), you run SPICE simulations with the parametric sweep.
This technique (except for parametric sweep plots) is well summarized in the introduction section of the article Automated netlist generation for 3D electrothermal and electromagnetic field problems.

In order to analyse complex electromagnetic (EM) problems, two main routes can be identified. First, a numerical approach for solving the full set of Maxwell ’s field equations offers the advantage of capturing all relevant effects but can be very demanding in terms of computational resources.
...
Secondly, one may use compact models to obtain an efficient
representation of a complex system. For example, electrical engineers
employ circuits to model and describe the behaviour of complex
devices.

The rest of the article is a detailed report of contrivances used to accomplish the circuit extraction, the coupling of EM and materials science equations, the elaboration of the description and implementation of boundary conditions and excitations, etc. The reference section, in itself, is a quite comprehensive review of the use of lumped-circuit-element model for solving integrated EM/materials science problems.
If you find this article technically difficult for understanding, I recommend to you a very good introduction into this technique: Electric circuit diagram equivalents of fields.