# Understanding Hysteresis Curves: Mathematical Modeling for Nonlinear ODEs

• mhill
In summary, hysteresis is a phenomenon where a system's response is influenced not only by its current input, but also by past inputs. Hysteresis curves are graphical representations of a system's output in response to varying inputs, typically exhibiting loops or irregular patterns due to nonlinearity. Mathematical modeling is important for understanding and predicting the behavior of nonlinear ODEs, which are commonly used to model complex systems in science and engineering. Some common methods for modeling hysteresis curves include Preisach, Jiles-Atherton, and Duhem modeling. Hysteresis curves can be used to model a wide range of systems, but the accuracy and applicability of the models may vary depending on the complexity of the
mhill
the idea is , if we have the magnetic field strength (H) and magnetic flux density (B) so we represent the 'hysteresis cycle' to be B(H)=B my question is could we deduce mathematically the hysteresis curve ?? for example if we can provide a model of a nonlinear ODE so

$$\frac{dB}{dH}= B^{r}- (1/B)$$

or something similar, i would be interested in the differential equation satisfied by B=B(H) thanks.

Since B(H) is not a single valued function, or any simple function, of H, you cannot do what you are trying.

I am fascinated by the concept of hysteresis curves and the potential for mathematical modeling to help us understand and predict their behavior. The proposed model, with a nonlinear ODE representing the relationship between magnetic field strength (H) and magnetic flux density (B), shows promise in capturing the complex and dynamic nature of hysteresis curves.

However, it is important to note that while mathematical models can provide valuable insights and predictions, they are not a perfect representation of the real world. There are many factors that can affect the behavior of hysteresis curves, such as material properties, environmental conditions, and experimental setup. Therefore, it is crucial to validate any mathematical model with experimental data to ensure its accuracy and applicability.

That being said, if we can provide a model of a nonlinear ODE that accurately represents the relationship between H and B, we can indeed deduce the hysteresis curve mathematically. This would allow us to study and analyze the behavior of hysteresis curves in a more systematic and quantitative manner, leading to a better understanding of their underlying mechanisms.

In conclusion, the idea of using mathematical modeling to understand hysteresis curves is a promising one, and I am eager to see further research and developments in this area. By combining theoretical models with experimental data, we can gain a deeper understanding of hysteresis and its implications in various fields such as materials science, engineering, and physics.

## What is hysteresis?

Hysteresis is a phenomenon in which the response of a system depends not only on its current input, but also on its past inputs. In other words, the output of the system may differ depending on whether the input is increasing or decreasing.

## What are hysteresis curves?

Hysteresis curves are graphical representations of how a system's output changes in response to a varying input. They show the relationship between the input and output over time, and often exhibit loops or irregular patterns due to the nonlinearity of the system.

## Why is it important to use mathematical modeling for nonlinear ODEs?

Nonlinear ODEs (ordinary differential equations) are often used to model complex systems in science and engineering. Mathematical modeling allows us to understand and predict the behavior of these systems, which is crucial for designing and optimizing processes and technologies.

## What are some common methods for modeling hysteresis curves?

Some common methods for modeling hysteresis curves include Preisach modeling, Jiles-Atherton modeling, and Duhem modeling. These methods use mathematical equations and parameters to describe the hysteresis behavior of a system.

## Can hysteresis curves be used to model any type of system?

Hysteresis curves can be used to model a wide range of systems, from mechanical and electrical systems to biological and economic systems. However, the accuracy and applicability of the models may vary depending on the complexity of the system and the chosen modeling method.

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