Skip to content
scikit-complexity
Core
Initializing search
georgedouzas/scikit-complexity
Overview
Models
API
Examples
Development
scikit-complexity
georgedouzas/scikit-complexity
Overview
Overview
User guide
Compatibility
Changelog
License
Models
Models
Physics
Physics
Active matter
Active matter
Active Brownian particles
Active Brownian particles with local alignment
Active Model B+ of motility-induced phase separation
Active Ornstein-Uhlenbeck particles
Active nematic and polar gels
Bertin-Droz-Grégoire kinetic flocking
Chiral active particles
Cucker-Smale flocking
Depot-pumped Brownian particles
Dry active nematics
Ginelli nematic particles
Grégoire-Chaté cohesive flocks
Keller-Segel chemotaxis
Living crystals
Microscopic flocking with aligning binary collisions
Motility-induced phase separation
Nonreciprocal Vicsek model
One-dimensional active viscoelastic and poroelastic gel with contractile cells
Run-and-tumble
Toner-Tu hydrodynamics
Vicsek model
Celestial mechanics
Celestial mechanics
N-body and solar system
Restricted three-body problem
Sitnikov problem
Störmer charge in a dipole field
Two-body orbit
Climate
Climate
Budyko-Sellers latitude model
Coupled soil and deep temperature maps
Daisyworld
Declining energy return on investment
ENSO delay oscillator
Gissinger geodynamo
Hasselmann stochastic climate
Lorenz-84
Lorenz-96
Network of interacting tipping elements
Rothman excitable carbon cycle
Saltzman-Maasch glaciation
Stochastic energy balance with bifurcation-, noise-, and rate-induced tipping
Stochastic fold with a ramped control parameter
Van der Pol ice ages
Zero-dimensional energy balance with ice albedo
Cosmology
Cosmology
Friedmann expansion
Criticality
Criticality
Bak-Tang-Wiesenfeld sandpile
Drossel-Schwabl forest fire
Evolutionary Sherrington-Kirkpatrick game
Forest fire on hexagonal lattices and graphs
Langevin field theory of absorbing-state transitions with a conserved energy field
Manna sandpile
SK game of reinforcement learners
Fluids
Fluids
BGK
Boltzmann
Burgers
Bénard-Marangoni convection with a free, thermocapillary surface
Decaying turbulence
Discrete-velocity Boltzmann gas of Carleman
Enskog equations
FHP lattice gas
Kuramoto-Sivashinsky
Rayleigh-Bénard
Shallow-water dam break
Vlasov
Wave-number conservation and wave breaking
Heat
Heat
Cooling coffee
Heat diffusion
Heat on an L-shaped domain
Mechanics
Mechanics
Ballistic pendulum
Bouncing ball
Circular billiard
Coupled pendulums
Double pendulum
Driven damped oscillator
Gyroscope in a gimbal
Harmonic oscillator
Huygens clocks and pendulums on coupled supports
Magnetic pendulum
Newton's cradle
Parametric pendulum
Particle in the well k x^2 e^-x
Pendulum
Pendulum on a sliding cart
Projectile
Rotating balls on rods
Rotating swing
Two-mass spring-damper between walls
Nonlinear oscillators
Nonlinear oscillators
Adler equation
Duffing
Dynamical billiards of Sinai and mushroom shapes
Forced Van der Pol
Hénon-Heiles
Stuart-Landau
Van der Pol
Oceanography
Oceanography
Quasi-geostrophic double gyre
Stommel thermohaline boxes
Pattern formation
Pattern formation
Allen-Cahn non-conserved relaxation (Model A)
Cahn-Hilliard phase separation (Model B)
Complex Ginzburg-Landau
Nonreciprocal Cahn-Hilliard
Swift-Hohenberg
Seismology
Seismology
Burridge-Knopoff spring-block fault
Olami-Feder-Christensen
Soft matter
Soft matter
Annealed transient time motion
Brownian particle near a wall
Continuous-time random walk
Diffusion in a speckle field
Fractional Brownian motion
Fully biased walk among quenched broad traps
Inertial and overdamped Brownian motion
Kramers escape
Langevin equation with colored noise
Lévy walk
Multiplicative noise conventions
On-off flashing ratchet
Optical trap including oscillating and blinking traps
Overdamped particle in a tilted periodic potential
Scaled Brownian motion
Shaken frictional spring-block chain
Stochastic resonance
Superdiffusive Levy flight
Statistical mechanics
Statistical mechanics
Asymmetric exclusion process with open boundaries
Bouchaud trap model
Contact process
Continuum percolation
Diffusion-limited aggregation
Discrete master equation
Dissipative zero-range process on a tree
Edwards-Anderson spin glass
Ehrenfest urn model of two boxes
Fully connected Ising model with Glauber dynamics
Fully connected branching and annihilation
Ideal gas
Ising
Ising on a graph
Landau mean-field relaxation
Lennard-Jones fluid
Mattis spin glass
Potts
Q2R reversible Ising automaton
Quantum Heisenberg model
Random energy model
Sherrington-Kirkpatrick spin glass
Site percolation
TASEP
Two-phase zone exchange
XY
Zero-range process
Synchronization
Synchronization
Aggregate-averaging synchronization
Coupled Rössler and the master stability function
Coupled map lattices on networks
Delayed Kuramoto
Globally coupled Stuart-Landau oscillators with frequency spread
Globally coupled systems with heterogeneous time scales
Kuramoto
Kuramoto on networks
Kuramoto oscillators with three-body coupling
Kuramoto-Sakaguchi chimera
Mirollo-Strogatz pulse-coupled oscillators
Nonlocal ring chimera
Ott-Antonsen reduction
Swarmalators
Winfree model
Waves
Waves
Schrödinger equation as real and imaginary fields
Schrödinger equation minimally coupled to an electromagnetic potential
Spring chains and guitar string
Standing waves on a string
Chemistry
Chemistry
Kinetics
Kinetics
Bistability on a catalyst pellet
Brusselator ODE
Chemical Langevin equation of the Schlögl reaction
Chemical Langevin equation of the enzyme network
Cubic autocatalysis
Cyclic cellular automaton
Hodgepodge machine
Michaelis-Menten as ODEs and as a jump process
Oregonator
Protein corona binding on a nanoparticle
Pulsed electrochemical reactor
Pattern formation
Pattern formation
Brusselator fields
Gray-Scott
Schnakenberg
Biology
Biology
Collective behaviour
Collective behaviour
Active walkers and trail formation
Binary ant decision
Bird swarm with pair potentials
Boids in two dimensions
Calm and nervous rats
Couzin shoal with repulsion, alignment, and informed leaders
Pheromone foraging
Ecology
Ecology
Agent-based Lotka-Volterra
Carrying capacity of a meadow
Competition
Droop cell-quota growth
Exponential growth
Fibonacci rabbits
Fisher-KPP
Food webs
Generalized Lotka-Volterra microbial community
Generalized stochastic predator-prey
Hutchinson
Intrinsic-instability populations
Logistic growth
Logistic growth with a varying capacity
Lotka-Volterra
Lotka-Volterra with harvesting
Mangrove succession
Mutualism
Neutral Moran model with speciation
Neutral birth-death with hopping between boxes
Neutral macroecology
Nicholson-Bailey
Random Lotka-Volterra with higher-order interactions
Rosenzweig-MacArthur and rate tipping
Sequentially linear ecosystem
Stigmergic predator-prey automaton
Wolf and sheep
Epidemiology
Epidemiology
Activity-driven temporal networks
Adaptive SIS with rewiring
Agent-based SIR with mortality, waning immunity, incubation, and lockdown
Degree-class SIR on uncorrelated networks
Discrete-time SIRS with a recovery delay
Heterogeneous mean-field SIS
Metapopulation reaction-diffusion
Quenched mean-field SIS
Random-walker epidemics on a grid and on a small world
SIR
SIR on a network as an agent model
SIR with optimal vaccination
SIRS
SIS
Evolution
Evolution
Adaptive climbing in finite populations
Bak-Sneppen
Eigen quasispecies
Hypercycles
Jain-Krishna autocatalytic networks
Moran process
NK fitness landscapes
Replicator dynamics and hawks and doves
Rock-paper-scissors
Solé-Manrubia extinctions
Strong-selection weak-mutation walk on fitness landscapes
Tangled Nature
Neuroscience
Neuroscience
Adaptrode synapse
Amari neural field
FitzHugh-Nagumo ODE
Hodgkin-Huxley
Integrate-and-fire
Izhikevich
Kinouchi-Copelli excitable network
LEGION oscillators
Networks of leaky integrate-and-fire neurons with delays
Polyhomeostatic neuron
Theta neurons and QIF networks
Wilson-Cowan
Winners-take-all network
Oncology
Oncology
Acquired and induced resistance with phenotype switching
Bone-marrow and blood cells with blasts and cancer stem cells
Cell-cycle compartments with killing, blocking, and recruiting agents
Core and periphery vasculature under anti-angiogenic therapy
Effector cells, tumour, and IL-2 under adoptive therapy
Exponential-linear tumour growth
Generalized logistic (Richards) growth
Glioma, glia, and neurons under temozolomide and virus
Gompertz growth
Gompertz growth with a vascular carrying capacity
Gompertzian cell-cycle phases under tamoxifen
Hahnfeldt model with effector cells, pharmacokinetics, resistance, and toxicity
Immune competition
Intermittent androgen suppression switched by PSA thresholds
Kirschner-Panetta model with TGF-beta and siRNA
Linear-quadratic cell survival and biologically effective dose
Linear-quadratic impulsive irradiation with a radiosensitizer
Multiscale tumour angiogenesis
Normal and leukaemic stem cells with feedback regulation
Normal and malignant stem-cell compartments with feedback and therapy
Normal and tumour competition under radiation
Normal, tumour, and immune cells under chemotherapy
Norton-Simon Gompertzian cell kill
Oncolytic adenovirus with T cells and dendritic-cell injection
Optimal adoptive therapy and IL-2 dosing
Optimal chemotherapy dosing
Paclitaxel and trastuzumab with antibody binding
Piecewise-linear intermittent androgen suppression
Power-law tumour growth
Predator-prey tumour-immune model of TCR gene therapy
Primary and secondary sites with a migration delay under chemotherapy
Prostate cancer driven by activated androgen receptors
Prostate cancer under continuous androgen suppression
Prostate cancer with an androgen cell quota and PSA
Red-cell production under 6-mercaptopurine
Resistance subpopulations under three drugs
Resting and hunting immune cells with a conversion delay under chemotherapy
Skipper-Schabel-Wilcox log-kill
T cells, tumour, and anti-PD-1 checkpoint inhibitor
T cells, tumour, dendritic cells, and IL-2 under dendritic-cell vaccination
Tumour and vascular volume under an angiogenesis inhibitor
Tumour, NK cells, CD8 T cells, and lymphocytes under chemoimmunotherapy
Tumour-immune model with dendritic licensing, IL-2, IL-10, and TGF-beta
Tumour-immune populations with division delays under dendritic-cell vaccination
Two tumour clones under chemotherapy and dendritic-cell vaccine
Uninfected and infected cells, virus, and chemotherapy
Uninfected and infected tumour cells under an oncolytic virus
Von Bertalanffy growth
Physiology
Physiology
Aliev-Panfilov cardiac tissue
Blood glucose stabilised by antagonistic insulin and glucagon loops
Coagulation cascade amplified by positive feedback and bounded by fibrinolysis
Cumulative drug toxicity
FitzHugh-Nagumo spirals
Intercellular exchange through gap junctions and tunnelling nanotubes on a cell network
Lumped cardiovascular model
Mackey-Glass
Stimulus-response, adaptive response, and anticipation with response, restore, repair, and preparedness costs
Substance exchange between logistic cells in a closed contour
Two-compartment pharmacokinetics
Systems biology
Systems biology
Adenylate cyclase kinase cascade amplifier with G-protein timer inactivation
Boolean model of the mammalian cell cycle
Boolean repressilator
Drosophila circadian clock
Generalized mass action and S-system power-law models
Genetic toggle switch
Goodwin oscillator
Kauffman random Boolean networks
Min-protein skeleton model as mass-conserving reaction-diffusion
Negative autoregulation and bursty gene expression
Probabilistic Boolean network
Repressilator
Three-gene Boolean network
Three-node phosphorylation oscillator
Yeast cell-cycle network
Economics
Economics
Econophysics
Econophysics
Boltzmann wealth exchange
El Farol
Exchange with debt limit and with saving propensity
Kinetic wealth and welfare dynamics
Kolkata Paise Restaurant
Minority game and its evolutionary version
Finance
Finance
Bouchaud-Mézard wealth
Correlated geometric Brownian motions
DebtRank cascades
Geometric Brownian motion
Gibrat
Kesten processes
Multiplicative
Order book with imitation
Random-walk traders with arbitrage
Innovation
Innovation
Arthur-Polak technology evolution
Bass diffusion
Combinatorial creative phase transition
Fixed-line phone adoption
NK technology model
Macroeconomics
Macroeconomics
Capital stock
Exchange rates in international trade
Firm and bank credit networks
Fractional-reserve banking
Metaphoria mortal hunter-gatherer and monetary economies
Multiplier-accelerator
Pontryagin capital and consumption
Solow
Stock-flow consistent monetary economy
Toy firm investment
Markets
Markets
Ajani's choice and fair food
Beer distribution game
Bilateral two-good trade on complete, isolated, and small-world networks
Brock-Hommes heuristic switching
Car wash queue
Car-dealer inventory with delays
Cobweb
Commodity cycle with capacity delay
Cournot duopoly with beliefs
Customers choosing between two shops of perishable goods
Double auction
Edgeworth and Red Cross barter
Labour market
Produce market
Riccati price adjustment
Shops and digital markets
Static oligopoly equilibria
Sugarscape
Toy and three-goods traders
Resources
Resources
Cocoa
Food security models
Harvesting farmers
Hilsa fishery
Oil economy
Optimal harvesting
Renewable fishery with capital
Tragedy of the meadow commons
Von Thünen land use
Social
Social
Cooperation
Cooperation
Iterated prisoner's dilemma tournament
Public goods game
Public goods game on hypergraphs
Spatial prisoner's dilemma with best-neighbour and Fermi imitation
Two-player games on links and three-body games on 2-simplices
Crowds
Crowds
Criminality and security
Crowd dynamics and evacuation
Social force pedestrians
Language
Language
Mandelbrot least-effort word frequencies
Opinion dynamics
Opinion dynamics
Axelrod culture dissemination
Belief diffusion with influentials
Coevolving voter
Cognitive consistency agents
Complex agents with internal states and standardization
Deffuant bounded confidence
Galam majority
Hegselmann-Krause
Join-a-club spins
Kinetic opinion formation
Majority rule automaton
Naming game
Nonlinear three-body consensus on temporal hypergraphs
Social impact theory
Sznajd
Threshold adoption
Voter model
Voter variants
Organizations
Organizations
Barabási priority queues
Bonabeau hierarchies
Brothel movement model
Employment takeover
Escalation
Gravity interaction model of urban scaling
Insider sabotage
Obesity model
Shifting the burden
Success to the successful
Segregation
Segregation
Schelling
Stochastic Schelling
Spreading
Spreading
Maki-Thompson rumours
SIS on hypergraphs with heterogeneous exposure and a nonlinear infection kernel
Simon-Yule growth
Simplicial contagion
Watts threshold cascades
Engineering
Engineering
Circuits
Circuits
Chua double and multiple scrolls
Circuits under periodic impulses
Memristor oscillator
Modified Chua with mixed-mode oscillations
RLC circuit
Tunnel-diode oscillator
Vibration energy harvester
Control
Control
Linear-quadratic regulated oscillator
PID governance loop
PID-stabilised inverted pendulum
Pendulum swing-up
Satellite transfer
Thermostat
Power systems
Power systems
Faraday-disk charger
Regenerative braking
Swing-equation power grid with Braess paradox
Wheel and rail contact
Processes
Processes
Bathtub
Cascade classifier
Food relief system
Irrigation system
Rice milling system
Solid waste system
Robotics
Robotics
Light-sensitive robots with sensory delay
Swarmtaxis
Traffic
Traffic
Car following with delay
Charbonneau traffic
GKT non-local traffic
Intelligent driver model
Kerner-Konhäuser model
Langevin car-following toward a density-dependent speed
Lighthill-Whitham-Richards
Moment equations of Langevin traffic with a jam instability
Nagel-Schreckenberg
Optimal velocity
Payne model
Ridesharing
Ring-road driver agents
Mathematics
Mathematics
Dynamical systems
Dynamical systems
Baker
Bernoulli doubling map
Cat map
Circle
Cubic chaotic map and its chaotic walk
Cusp normal forms
Finite-time blow-up
Generalized tent map
Hopf
Hénon map
Intermittency maps
Logistic map
Lorenz
Newton-Raphson map
Quadratic system with a slow manifold and a finite Koopman embedding
Rössler
Rössler with an Ornstein-Uhlenbeck control parameter
Saddle-node
Sprott jerk
Standard
Subcritical Hopf normal form
Takens-Bogdanov
Tent
Towel maps
Fractals
Fractals
Cantor
Iterated function systems by the chaos game
Julia sets
Koch
Mandelbrot set
Sierpiński substitutions
Fractional dynamics
Fractional dynamics
Fractional Lorenz
Fractional Van der Pol
Fractional damped oscillator
Fractional relaxation
Networks
Networks
Barabási-Albert growth
Centralities, assortativity, communities, and motifs
Diffusion
Erdos-Renyi and Watts-Strogatz graphs
Growing simplicial complex by triangle attachment
Holme-Kim growth
PageRank iterations on networks
Random failures and targeted attacks on networks
Random walks
Size-biased random walk on hypergraphs
Triadic percolation
Vertex-copying network growth
Stochastic processes
Stochastic processes
Ageing random walk
Bernoulli process
Birth-death process and M/M/1 queue
Fragmentation
Galton-Watson branching
Hidden Markov source
Markov source
Ornstein-Uhlenbeck with weakening restoring force
Persistent random walk
Poisson process
Pólya urn
Random walk with autoregressive velocity
Random walks
Sample-space-reducing process
Stochastic on-off intermittency
Computer science
Computer science
Automata
Automata
Automata on the Grigorchuk group
Automata on the free group
Baumslag-Solitar groups
Diffusion automaton
Elementary automata
Game of Life
Heisenberg
Highlife and the planar automaton zoo
Lamplighter
Langton's ant
Linear automata over rings
Noisy automata
Subshifts
Unbounded-alphabet automaton
Evolutionary computation
Evolutionary computation
Bit-string evolution on a fitness landscape
RobbyGA can collector
Simulated annealing, genetic algorithms, and differential evolution
Neural networks
Neural networks
Asymmetric diluted Hopfield network
Binary perceptron and random K-SAT
Echo state network
Elman recurrent network trained by backpropagation
Hopfield network
API
API
Base
Errors
Types
Analysis
Analysis
Types
Core
Core
Base
System
Types
Elements
Interactions
Laws
Laws
Utils
Spaces
Specs
Engine
Engine
Types
Backends
Compile
Compile
Passes
Problems
Runtime
Solvers
Viz
Experiments
Experiments
Types
Specs
Models
Models
Types
Biology
Biology
Collective behaviour
Common
Common
Excitable
Kinetics
Networks
Pharmacokinetics
Populations
Stigmergy
Ecology
Epidemiology
Evolution
Neuroscience
Neuroscience
Types
Oncology
Physiology
Systems biology
Systems biology
Types
Chemistry
Chemistry
Common
Common
Kinetics
Kinetics
Pattern formation
Computer science
Computer science
Automata
Evolutionary computation
Neural networks
Economics
Economics
Common
Common
Forecasting
Resources
Econophysics
Finance
Innovation
Macroeconomics
Markets
Resources
Engineering
Engineering
Circuits
Common
Common
Mechanics
Control
Power systems
Processes
Robotics
Traffic
Mathematics
Mathematics
Common
Common
Flows
Dynamical systems
Fractals
Fractals
Types
Fractional dynamics
Networks
Stochastic processes
Stochastic processes
Types
Physics
Physics
Active matter
Celestial mechanics
Celestial mechanics
Types
Climate
Common
Common
Fields
Mechanics
Oscillators
Particles
Quantum
Spins
Cosmology
Criticality
Fluids
Heat
Mechanics
Nonlinear oscillators
Oceanography
Pattern formation
Seismology
Soft matter
Statistical mechanics
Synchronization
Waves
Social
Social
Cooperation
Crowds
Language
Opinion dynamics
Organizations
Segregation
Spreading
Specs
Examples
Examples
Physics
Physics
Heat
Heat
Cooling coffee
Nonlinear oscillators
Nonlinear oscillators
Duffing
Synchronization
Synchronization
Mirollo-Strogatz
Chemistry
Chemistry
Kinetics
Kinetics
Brusselator
Cubic autocatalysis
Cyclic cellular automaton
Biology
Biology
Epidemiology
Epidemiology
Agent-based SIR
Evolution
Evolution
Replicator dynamics
Systems biology
Systems biology
Boolean repressilator
Economics
Economics
Finance
Finance
Correlated geometric Brownian motions
Geometric Brownian motion
Resources
Resources
Fishery capital
Social
Social
Cooperation
Cooperation
Public goods game on a hypergraph
Prisoner's dilemma tournament
Opinion dynamics
Opinion dynamics
Hegselmann-Krause
Engineering
Engineering
Circuits
Circuits
Chua's circuit
Memristor oscillator
Tunnel-diode oscillator
Mathematics
Mathematics
Dynamical systems
Dynamical systems
Finite-time blow-up
Fractals
Fractals
Julia set
Networks
Networks
Random walk on a hypergraph
Computer science
Computer science
Automata
Automata
Game of Life
Majority automaton on the Baumslag-Solitar group
Majority automaton on the free group
Development
Development
Contributing
Code of Conduct
Table of contents
core
Core
What a system is: elements, interactions, laws, space and the system itself.
Back to top