Dynamical System Assignment Homework Help

A Dynamical System is a system whose state evolves with time over a state space according to a fixed rule. A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on another object. When the reals are acting, the system is called a continuous dynamical system, and when the integers are acting, the system is called a discrete dynamical system.  A dynamical system is a concept in mathematics where a function describes the time dependence of a point in a geometrical. System of mathematical equations is where the output of one equation forms a part of the input of another.


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Our dedicated team of Professionals has helped a number of students pursuing education through regular and online Universities, Institutes or Online tutoring in the following topics-

  • Adiabatic invariants, Poincare sections, area preserving mappings
  • Autonomous and non - Autonomous system
  • Belousov-Zhabotinskii reaction
  • Bifurcation theory and normal forms
  • Block Diagrams and PD Control, Integral Control and Root Locus.
  • Bode's sensitivity integral
  • Calculation and interpretation
  • Chaos and fractals
  • Classical system inputs/commands/disturbances
  • Classification of singular points
  • Cobweb diagrams
  • Concept of state and state-space modeling of dynamic systems
  • conservative versus dissipative systems
  • Coupled oscillators
  • Crises, crisis induced intermittency, strange non chaotic attractors
  • critical point analysis
  • Damped and undamped dynamical system
  • Degrees of stochasticity: ergodicity, mixing, K, C. and Bernoulli systems
  • Deterministic chaos
  • Diffeomorphisms and flows
  • Discrete and continuous dynamical system
  • Driven and coupled pendulum
  • Dynamics of infectious diseases
  • Effects of Disturbances on Control Systems
  • Elementary classification of bifurcations for maps and flows
  • Elementary ideas on  perturbation theory
  • Elements of symbolic dynamics
  • Equilibrium points and their stability
  • Evasion in predator-prey systems
  • Examples of dynamical systems in the life sciences
  • Feedback Control: Proportional, PI, PD, and PID Controllers
  • Feedback stabilization
  • Firefly flashing, Kuramoto model
  • First Order Frequency Response
  • First Order Time Response
  • Fisher's equation
  • FitzHugh-Nagumo model for neural impulses
  • Fixed points and linearization
  • Flow operators and their classification: contractions, hyperbolic flows, expansions, manifolds: stable and unstable
  • Frequency response of systems
  • Frobenius Perron equation, invariant density
  • Global bifurcations
  • Growth and control of brain tumours
  • H2 optimization, H∞ optimization
  • Hamiltonian systems
  • Index theory
  • Invariant manifold techniques
  • kinetics of plane motion
  • Laplace Transform and Transfer Functions
  • Least square solutions of linear problems
  • Liapunov exponent
  • Linear and nonlinear evolution equations: Flows and maps
  • Linear and nonlinear systems of ordinary differential equations in rn
  • Linear autonomous systems. Phase plane analysis of 2D systems
  • Linear stability analysis
  • linear, angular impulse-momentum principles, vibrations
  • Local and Global Stability
  • Matched asymptotic expansions
  • Mathematical analysis
  • Measures of chaos. Liapunov exponents. Fractal sets and dimensions
  • Michaelis-Menten kinetics
  • Michaelis-Menten-type enzyme kinetic
  • Minimal realizations
  • Modeling of Mixed Systems
  • Modeling systems using simultaneous differential equations
  • Models of neural firing
  • Molecular and cellular biology
  • Multifractals, generalized dimensions, K S entropy
  • Multiple-scale dynamics
  • Newton’s laws of motion
  • Nonlinear systems, stability of equilibria and lyapunov functions
  • Numerical solutions increase understanding
  • One dimensional maps
  • Open and Closed Loop Feedback
  • Oscillations in biochemical systems
  • Oscillations in population-based models
  • Partial differential equations
  • Particle, rigid body kinematics
  • Period doubling route to chaos
  • Perturbation techniques
  • phase trajectories and their properties
  • Pitchfork bifurcation
  • Poincare Bendixson theorem
  • poincare-bendixson theorem and limit cycles
  • Quasiperiodicity and mode locking
  • Reaction-diffusion equations
  • Rigid body problems using work-energy
  • Root-Locus Technique
  • Routes to chaos in dissipative systems
  • Saddle bifuration- period doubling and Hopfbifuration
  • Second Order Frequency Response
  • Single Input-Single Output Systems
  • Singular perturbation theory
  • Solutions of state-space models
  • Stable, Unstable, Centre manifolds
  • State-Space Models of Systems
  • Strange attractors: Lorentz and Rossler attractors
  • Structural stability and hyperbolicity
  • System Dynamics and Control
  • System input and output relationships
  • System Order and relationship to energy storage elements
  • The Role of the Laplace Transform
  • The special case of flows in the plane
  • Time Response Analysis of Linear Dynamic Systems
  • Transcritical and Pitchfork bifurcations
  • Travelling wave solutions
  • Turing bifurcations , Chaos, Population dynamics